Roadmap

Stage 1: Regular Playthrough

Play through the game regularly, grabbing as many Lums and rescuing as many Teensies as you can.  Although it differs on a level-to-level basis, there's generally 10 Teensies per level and you'll need 600 Lums to grab the gold trophy and the scratch ticket.

As you progress through the game, you'll unlock all four Challenges after hitting Awesomeness 7.  Be sure to start participating in these challenges right away!  It will lessen the grind needed to obtain the final Awesomeness level.
Free The Barbarian princess
Complete the "Castle Rock" painting
Complete the "Orchestral Chaos" painting
Complete the "Mariachi Madness" painting
Complete the "Gloo Gloo" painting
Complete the "Dragon Slayer" painting
Get rid of the five Dark Teensies
Complete the "Living Dead Party" world
Rescue the 10 princesses
Collect enough lums to unlock 10 Heroes paintings in the Heroes Gallery
Break all the locks on the worlds' and levels' paintings
Save enough Teensies and get rid of the Dark Teensies to make all the Invasion paintings appear
Finish your first "Back to Origins" painting
Finish all the "Back to Origins" paintings
Unlock all the Challenge paintings

Stage 2: Cleanup

After beating the main game, go through and clean up any stages that do not have all Teensies unlocked or gold trophies.  During this process, you should unlock the remaining scratch tickets, creatures, and Lums.

If you had missed a few of the various level/kill count trophies, nab those now.  The goal here is to have all 700 Teensies unlocked, all World Diamond Cups, and all Gold Trophies (from grabbing Lums, not from rescuing Teensies) before we move to finish up the last remaining Awesomeness level.
Rescue all the kidnapped Teensies
Win and scratch all the lucky tickets
Win all the creatures
Go fast enough to save 3 Teensies in an Invasion painting
Get the 3 lums cups and the 3 Teensy cups of a painting
Save all the Teensies in one world to win a Diamond Cup
Win all the Bronze Cups from the paintings
Win all the Silver Cups from the paintings
Win all the Gold Cups from the paintings
Win all the Diamond Cups from the World paintings
Pull a turnip out of the ground with a crush attack, then hit it with a jump kick
Kill 5 enemies using turnips
Pull 100 turnips out of the ground
Stand on top of an enemy with a shield until he tries to attack you
With Barbara or Elysia, slide on your axe for 30 meters
Destroy the parachutes of 5 enemies to make them fall
Get rid of 100 enemies with the Flying Punch
In one run of "Lucha Libre Get Away", let the Luchador kill 10 enemies for you
Collect all the lums flying above the bouncing island in "The Mysterious Inflatable Island"
Kill 10 Toads using their electric projectiles
Go through "Mansion of the Deep" without crossing any light from a Dark Sentry or touching any laser
Destroy 5 Rubber Ducks sent by Sharkmen

Stage 3: Challenges + Awesomeness Level

This is the most time demanding section of the platinum.  After doing everything else, you'll still be somewhere near 1500 points shy of your final Awesomeness level.  In order to make up those last 1500 points, you'll have to take to the challenges.

There are four challenges:  two weekly challenges and two daily challenges.  Each bronze trophy earned in the challenges is worth 1 point, while silvers are worth 5 and golds are worth 10.  Diamond ranks are worth 50, but you have to place in the top 1% in order to earn it, so it's not entirely feasible.

Realistically, plan on earning about 10-15 points per day from the daily challenges, and about 15-20 per week from the weekly challenges.  As far as that stands, you're looking at about 3 months (!) of daily and weekly challenges. At the very least, it will give you ample time to knock out the "The Competitor" trophy.
Gather 1 million lums and unlock the final Hero
Take part at least once in the 4 different Challenges
Win a Bronze cup at the end of a Challenge
Win a Gold cup at the end of a Challenge
Beat one of your friends' scores in a Challenge
Beat your friends' scores in the Challenges 30 times
Reach the final level of Awesomeness
Legendary
Win all trophies in the game!
4.14%
Ultra Rare
Platinum
Barbara's Free!
Free The Barbarian princess
67.32%
Common
Bronze
Barbara's the first princess you can unlock.  Complete the stage behind her door to earn this trophy.
Rock that castle!
Complete the "Castle Rock" painting
47.59%
Uncommon
Bronze
This is the final painting in "Teensies in Trouble", the first level.  Complete this musical level and the trophy is yours.
Orchestrate this!
Complete the "Orchestral Chaos" painting
35.93%
Uncommon
Bronze
This is the final painting in "Toad Story", the second world.  Complete this musical level and the trophy is yours.
Mad world!
Complete the "Mariachi Madness" painting
30.40%
Uncommon
Bronze
This is the final painting in "El Fiesta de la Muerte", the third world.  Complete this musical level and the trophy is yours.
Splash!
Complete the "Gloo Gloo" painting
26.40%
Uncommon
Bronze
This is the final painting in "20,000 Lums Under the Sea", the fourth world.  Complete this musical level and the trophy is yours.
Dragon Rider!
Complete the "Dragon Slayer" painting
22.60%
Uncommon
Bronze
This is the final painting in "Olympus Maximus", the fifth world.  Complete this musical level and the trophy is yours.
Journey to the moon
Get rid of the five Dark Teensies
22.78%
Uncommon
Silver
You "fight" one of each of the Dark Teensies after fighting the bosses in each of the worlds.  You'll unlock this briefly after finishing the boss in the 5th world, Olympus Maximus.
World Tour!
Complete the "Living Dead Party" world
15.09%
Rare
Gold
The "Living Dead Party" world consists of one new musical level and six "remixed" musical levels.  These levels are the same, bar two exceptions:
  • Full screen filters will attempt to make the level harder by pixelating the screen, adding visual distortion, or even multiplying the screen.
  • They contain no checkpoints;  each level must be done entirely in one pass.

Generally speaking, they're not too tough, but it helps greatly to turn up the audio and listen for musical cues to help.
Princess savior!
Rescue the 10 princesses
17.48%
Rare
Silver
To rescue princesses, you must first earn enough Lums to unlock the doors to their respective stages.  Once unlocked, you have to beat a short stage in order to actually unlock the princess.

The last princess' stage is unlocked at 290 Lums.
Teensies' friend
Rescue 150 Teensies
35.91%
Uncommon
Bronze
See Gold The chosen one for more information.
Teensies' hero
Rescue 300 Teensies
24.61%
Uncommon
Silver
See Gold The chosen one for more information.
The chosen one
Rescue all the kidnapped Teensies
8.99%
Very Rare
Gold
In order to rescue all Teensies, you'll have to liberate all of the Teensies from the levels in addition to the Teensies from the scratch cards, which you'll unlock naturally as you complete the levels.

There's a great written guide here (courtesy of IGN) that has locations of all the Teensies hidden throughout the areas, as well as tips for some of the tougher Invasion levels.
Lucky!
Scratch 10 lucky tickets
47.90%
Uncommon
Bronze
See Silver Scratch me! for more information
Scratch me!
Win and scratch all the lucky tickets
9.20%
Very Rare
Silver
You get scratch tickets for obtaining 3/4ths of the Lums required for a gold trophy in a level and for completing a set of levels.  You'll unlock this naturally as you're working towards "The chosen one".
We could be heroes
Collect enough lums to unlock 10 Heroes paintings in the Heroes Gallery
23.24%
Uncommon
Bronze
You'll unlock playable characters as you gather Lums. To unlock 10 different characters, you'll need 100,000 Lums.
Sooo rich!
Gather 1 million lums and unlock the final Hero
5.50%
Very Rare
Silver
The odds are you won't earn one million Lums while playing through the game normally, so it's best to rely on the Lums earned through the challenges. It will work hand in hand with the grind towards Awesomeness 11.
They're so cute!
Win 30 creatures
19.57%
Rare
Bronze
See Silver I just love them! for more information.
I just love them!
Win all the creatures
9.71%
Very Rare
Silver
You'll nab all the creatures as you scratch off tickets.
Master of the locks
Break all the locks on the worlds' and levels' paintings
11.88%
Rare
Bronze
To unlock this trophy, you'll have to do the following:
  • Save 400 Teensies to unlock the Living Dead Party world, and then complete it.
  • Scratch enough tickets to unlock all of the Origins paintings.
  • Defeat all five world bosses and the evil Teensies (see Silver Journey to the moon).
Invaders!
Save enough Teensies and get rid of the Dark Teensies to make all the Invasion paintings appear
19.90%
Rare
Bronze
If you've been playing through Rayman Legends while collecting most of the Teensies in each level, you should unlock this as you defeat the last Dark Teensie.  If not, simply work on collecting more Teensies until this one unlocks.
That was fast!
Go fast enough to save 3 Teensies in an Invasion painting
29.63%
Uncommon
Bronze
You simply need to clear an Invasion painting in under 40 seconds, which admittedly is not as easy as it sounds.  However, a few practice runs should be sufficient in order to understand how the level works.
Perfect!
Get the 3 lums cups and the 3 Teensy cups of a painting
68.76%
Common
Bronze
On any level, rescue all of the Teensies (10 or 3, depending on the level) and earn enough Lums to grab the gold cup (600,  300, or 100) to nab this Trophy.
Swiped clean!
Save all the Teensies in one world to win a Diamond Cup
16.14%
Rare
Bronze
You won't be able to unlock this Trophy until you unlock all of the invasion levels.  Afterwards, just save all the Teensies in each painting in a single world to unlock this Trophy.
Bronze Addict
Win all the Bronze Cups from the paintings
9.37%
Very Rare
Bronze
See Bronze Gold Addict for more information.
Silver Addict
Win all the Silver Cups from the paintings
9.11%
Very Rare
Bronze
See 671e91.png Gold Addict for more information.
Gold Addict
Win all the Gold Cups from the paintings
7.52%
Very Rare
Bronze
This is a little different than Silver Diamond Addict.  You still have to rescue all 10/3 Teensies from each level, but you also have to earn 600/300/100 Lums in each level to unlock the Gold Trophy (the last tier, after the Scratch ticket tier).  The added Lum requirement makes it a bit trickier, as some levels can be a bit annoying.

Here are a few tips to maximize your Lum count in each level:
  • Rescue all Teensies.  In addition to the 25 Lums you get from actually saving the Lums, you stand to potentially earn a lot more from the stages to rescue the Royal Teensies (the Teensies you save after entering a hidden door).
  • Don't get hit.  This seems like an obvious one, but grabbing a heart while you still have one gives an extra 5 Lums.
  • Hit turnips/cages immediately after ground pounding.  Hitting it before it hits the ground will double the Lums earned from it.
  • Kill all enemies.  Each enemy gives at least 5 Lums, therefore skipping enemies can potentially cut you out of a good number of Lums.

This trophy includes ALL levels, including the ones behind princess doors and invasion levels.
Diamond Addict
Win all the Diamond Cups from the World paintings
9.00%
Very Rare
Silver
This is virtually the same as Gold The chosen one except it doesn't include the Teensies earned from scratch cards.
Nostalgia
Finish your first "Back to Origins" painting
42.74%
Uncommon
Bronze
See Silver Old school for more information.
Old school
Finish all the "Back to Origins" paintings
11.29%
Rare
Silver
You won't be able to complete all of the Origins levels until you unlock them via scratch cards (see Silver "Scratch me!").

Once you've unlocked them, simply complete the levels in any order to unlock this trophy.
Turnip combo
Pull a turnip out of the ground with a crush attack, then hit it with a jump kick
92.37%
Common
Bronze
Ground pound (Down + Square) a turnip and jump and kick it before it lands to earn this.  Bonus:  Doing this will give 10 Lums instead of 5.
Strike!
Kill 5 enemies using turnips
29.06%
Uncommon
Bronze
Unearth a turnip with a ground pound (Down + Square) and kick it towards an enemy.  If it collides, it will kill them.  Repeat four more times for the trophy.
Gardener
Pull 100 turnips out of the ground
26.80%
Uncommon
Bronze
Ground pound (Down + Square) the buried turnips throughout the stages.  This should come automatically as you work on unlocking all 700 Teensies (as some of them are buried in the turnip spots).
This ain't a platform!
Stand on top of an enemy with a shield until he tries to attack you
22.45%
Uncommon
Bronze
Jump and hover over one of the shield-toting goblins and he should raise his shield.  Stand on said shield until he motions to attack, at which point the trophy should unlock.
Axe skater
With Barbara or Elysia, slide on your axe for 30 meters
12.68%
Rare
Bronze
This trophy can actually be obtained on the first level.  First, choose either Barbara or Elysia (the two princesses unlocked from Teensies in Trouble) and then head to Once Upon a Time, the first level.  Immediately make your way to the right until you hit the first hill, then run to the left from the hill.  Crouch near the apex of the hill and hold it until you stop sliding.
Bad joke
Destroy the parachutes of 5 enemies to make them fall
49.36%
Uncommon
Bronze
You'll deal with lots of parachuting enemies in Toad Story.  During any section with an updraft (where you're able to float), just punch the parachute of a parachuting enemy. 

You should unlock this trophy without really even trying for it.
Shoot them up!
Get rid of 100 enemies with the Flying Punch
36.03%
Uncommon
Bronze
This should come naturally as you progress, but if for some reason it doesn't, this is extremely easy to accomplish on "When Toads Fly" in Toad Story.  You're gifted the Flying Punch at the beginning of the level.
Let him do the job
In one run of "Lucha Libre Get Away", let the Luchador kill 10 enemies for you
9.70%
Very Rare
Bronze
In "Lucha Libre Get Away", you'll be pursued by a number of Luchadores.  On your path will be a number of skeleton baddies.  Rather than deal with them yourself, simply jump over (or otherwise avoid them) and let the Luchador take care of them for you. 

There are a few skeletons that are difficult to avoid, but you don't need to avoid all of them.
Bouncing Island
Collect all the lums flying above the bouncing island in "The Mysterious Inflatable Island"
17.53%
Rare
Bronze
"The Mysterious Inflatable Island" is the first level in 20,000 Lums Under the Sea.  You'll start off on the eponymous island itself, but the Lums won't appear until you ground pound (Down + Square) the island.  After that point, the Lums will appear over the island.  They don't need to be collected in order for the trophy to appear and they will circle back around if you miss a few the first time around.
Watch out!
Kill 10 Toads using their electric projectiles
16.76%
Rare
Bronze
The best level to work towards this is "Elevator Ambush" in 20,000 Lums Under the Sea.  During the first elevator ride, simply dodge the Toads' projectiles and let them either hit themselves or another Toad.  The projectiles will bounce off of walls, so be careful.
Splinter Ray
Go through "Mansion of the Deep" without crossing any light from a Dark Sentry or touching any laser
8.27%
Very Rare
Bronze
This trophy isn't as bad as it seems, but it's still a pain in the ass.  The objective is to get through "Mansion of the Deep" without being spotted by a Dark Sentry (the things that shoot out the green light) or touching the lasers.  For this attempt, do not attempt to grab any extraneous Teensies or Lums.  Both paths (left and right at the start of the level) do not have any Dark Sentries or lasers until you deactivate the power. 

The left path only really has dangerous Dark Sentries during the underwater part.  The fishtank area has you go up and around the Dark Sentries. 

The right path is more straightforward during the underwater part:  hit the power switch and swim directly down.  In the next room, walljump in the first narrow opening and take the chain, jumping in the gap where you'd hit the Teensie cage.  The next room has two patrolling Dark Sentries, but they're easily predictable as long as you don't rush.

The laser room is the difficult part.  Carefully watch how each laser moves before deciding on how to approach it.  Each laser section has a tiny break in it, so don't feel obligated to rush through it.  The trickiest part is about halfway through, where there's a walljump section with a rising laser.

If a Dark Sentry goes red or you get zapped by a laser, back out entirely and restart.  Attempting to restart a section does not work.

If you're more of a visual person, below is a video that walks through how to obtain the trophy.


Splinter Ray Video Guide

Rubber Ducks
Destroy 5 Rubber Ducks sent by Sharkmen
9.71%
Very Rare
Bronze
An easy spot for this is right after the first elevator ride in "Elevator Ambush" in 20,000 Lums Under the Sea.  You'll come to a Sharkman tossing junk into a pile.  There's a platform right above a floating Teensie cage.  Carefully watch what the Sharkman throws:  if it's electrocuted, get ready to jump.  When he throws a rubber duck, however, just hit it before it hits you. 
Just kick it!
Win one Kung Foot game
32.76%
Uncommon
Bronze
This is the only trophy in the game that requires two controllers (or one controller and a Vita).  Once two controllers are connected, enter the Kung Foot painting and hit Options on the second controller to join in.  Once both players are in, simply win the game with the first controller to unlock this trophy.
Challenger!
Unlock all the Challenge paintings
28.40%
Uncommon
Bronze
You unlock the last challenge, the Weekly Xtreme, at Awesomeness 7.
Everywhere!
Take part at least once in the 4 different Challenges
18.21%
Rare
Bronze
Take part in each of the four challenges at least once:
  • Daily
  • Weekly
  • Daily Xtreme
  • Weekly Xtreme

They do not need to be done all in one day, but you should be doing the four challenges at the beginning of each week and the two dailies every day.
First steps
Win a Bronze cup at the end of a Challenge
36.80%
Uncommon
Bronze
To get a bronze trophy, you simply have to place in the top 90 percent.  It's honestly pretty easy.
On the way to the top!
Win a Silver cup at the end of a Challenge
27.85%
Uncommon
Bronze
To obtain a silver trophy, you have to place in the top 50 percent of the challenge.
A true champion
Win a Gold cup at the end of a Challenge
16.59%
Rare
Bronze
To nab a gold, you have to place in the top 20 percent of the challenge.  It's easier to do these on the daily challenges as opposed to the weekly, since the scores are less likely to move.
I'm ahead!
Beat one of your friends' scores in a Challenge
11.13%
Rare
Bronze
See Silver The competitor for more information.
The competitor
Beat your friends' scores in the Challenges 30 times
6.51%
Very Rare
Silver
In the Challenges, you'll see ghosts of your friends. Simply beat their scores 30 times to earn this trophy. Each friend counts as one towards the trophy, so the more friends you have doing challenges the quicker you'll obtain this.

Furthermore, you can also create a second profile, add that profile to your friends list, and then have that profile score very lowly, making it easy to overtake its score.

Thanks HappyKastanie for the tip regarding a second profile!
Truly awesome!
Reach the final level of Awesomeness
4.30%
Ultra Rare
Silver
This is it:  the big one.  The grind tag does not come lightly, but rest assured, the path to Awesomeness 11 is every bit a grind.

It works like this:  every day, there are two challenges you can complete for cups.  Every week, there are two more challenges you can complete starting Monday.  Both of these types of challenges give the same amount of points towards Awesomeness levels.

The daily challenges are where you'll be gaining most of the points needed.  Depending on how well you place in these challenges, you'll take home one of four cups:
  • Bronze Cup - top 90% - 1 point
  • Silver Cup - top 50% - 5 points
  • Gold Cup - top 20% - 10 points
  • Diamond Cup - top 1% - 50 points

Realistically, Diamond Cups are out of the equation.  The rule of thumb that I've used for challenges is around 10-15 points per day (a Gold Cup and a Silver Cup).  Even at that rate, you're looking to spend approximately the next 90 days doing daily challenges (provided you didn't start challenges as soon as you were able).