This is awarded for completing the game on Proud Mode or Critical Mode. The easiest way to get this is to complete it on Proud Mode. You will have to complete the game on Critical Mode to complete all the objectives. It's a short game so this isn't the most difficult trophy since the game has a lot of checkpoints. If you know the bosses well you can easily complete this. 

The most difficult things about the Critical Mode run are the enemy Heartless and the last boss. You can always escape the Heartless by running past them. But this will mean that you are a bit underleveled. But this is no problem. You can still easily beat the game while lvl 53-55.

Here is a guide for some strategies for each boss. The strategies assumes that it is on Critical Mode:

Castle Town - Demon Tower:
This is the first boss and it is not insanely difficult. It does not have much hp. Simply hit as much as you can. Remember your Shotlock, fire, and keep mp for healing. When you see it glowing red then get away. If it attacks as one unit the dodge. If it spreads out into many Shadows then wait until the sorround you and then block.

Alternatively; here is an additional video guide with slightly different strategies if that fits you better:

Demon Tower (Critical Mode)

Credit to TheDvsBstd for the video.

The World Within - Phantom Aqua:
This is the last phantom Aqua fight. You should be familiar with the way of killing her since by this time you have already killed her without getting hit. If it is too difficult follow the strategies from Objective 41 in  Ambitious.

Alternatively; here is an additional video guide with slightly different strategies if that fits you better:

Phantom Aqua (Critical Mode)

Credit to TheDvsBstd for the video.

Forest of Thorns - Darkside:
This is the boss fight of the Forest of Thorns. You should be familiar with the way of killing since by this time you have already killed it without getting hit too. If it is too difficult follow the strategies from Objective 47 in the Ambitious trophy. The only difference is that there are more lazers and the move faster. They have the same pattern every time but not the exact same pattern as the other difficulties.

Alternatively; here is an additional video guide with slightly different strategies if that fits you better:

Darkside (Critical Mode)

Credit to D0gSkwad for the video.

Final Boss - Demon Tide:

This is the hardest boss on Critical Mode and also the last, except for Phantom Aqua. It has 2 main phases and can sometimes be very aggressive with not leaving much room for attacking. When you enter the battle immediately go for 2 combos on the Demon Tide. You can see that it is about to attack when it glows red. Remember to save your Shotlock for the second phase

It will mostly fly up into the air. From here it can fly down into the ground. Here you have to look at the ground and follow it. When it jumps up it will jump towards you. Roll away just before it hits. You can see which way it moves by looking on the ground. The dust tracks its movements. It can also do 3 charged attacks against you. When it does this you can avoid in 3 ways:

1. The first is by blocking when it is close to you. There's more time between the first and the second attack than between the second and the third. 

2. You can also just make a double jump in good time before the attack. This seems a little inconsistent at the third attack because you don't always have the time to do a double jump. 

3. The last way is jumping up and then keep spamming  for block. This keeps you in the air above the attack.

It can also throw smaller Shadows after you. In this case either block them or keep dodging away from them. Use Wayfinder as soon as it gets available and then when the Demon Tide is locked in chains keep attacking it until the last second before you use the Finish command. 

Now it should transform to second phase in which you open up with the Shotlock. Try to get 3 Excellent ratings and then fire the rest of your focus bare with Shotlock immediately after. It will now be in a tornado formation. When it turns red you know it will attack. If it starts spinning then use block. If it throws Shadows at you either dodge spam away or block.

At one point it will go into an invincible phase where it shoots balls into the air and up from the ground. When this happens dodge as fast as you can. Then you will be thrown up into the air. Here you should spam your air dashing or spam your blocking. If you get hit once heal with either item or your magic because this can kill you in 2 hits.

After this phase you should be able to get the last remaining combos in to kill the Demon Tide. If you can use Spellweaver then do it. Firaga does quite a lot of damage, and you can spam it so fast. You will probably not get this in your first try. I beat it while level 56 so you don't have to grind levels to beat it.

Alternatively; here is an additional video guide with slightly different strategies if that fits you better. Note that it has a very good strategy for the Wayfinder part which makes all of phase 2 skippable which is pretty neat considering it's a very hard phase:

Demon Tide (Critical Mode)

Credit to ShinyMag for the video.