Note: This is the only trophy that you won't obtain naturally while progressing the story, but it's very hard to miss and there are 5 total eggs you can hatch, on the off chance you lose one somehow.There are 5 places where you can find a Cuddlefish egg:

1. On the floor in the Degasi base in the Deep grand reef.
2. Directly in the centre of a sinkhole in the Dunes.
3. On a table in the Lost river laboratory.
4. Within a cave in the Northeastern mushroom forest.
5. Within a cave in the Northwestern mushroom forest.

To get this trophy, you'll be using the egg from the Degasi base in the Deep grand reef. Follow the video in the guide for  Seamonsters to find the base. Scan the Alien containment on the top floor, then go down the ladder and pick up the Creature egg on the second floor. Once you've done those two things, head back to your base.

If you haven't got a spare room in your base, build a Multipurpose room above, below, or to the side of an existing room. If you're building it above an existing room, make sure you have room to place a ladder close to the walls on the inside of the room. Once you have an empty spare room, you'll be ready to craft an Alien containment in the centre of it. To do so, you will need 5 glass and 2 titanium. After that, you have to build a Hatch into the side of the containment using 1 quartz and 2 titanium.

When you have a fully built alien containment, climb in using the hatch, go into your inventory and drop the Cuddlefish egg. The egg will take around 20 minutes to hatch, so go and do something else while you wait (remember to keep an eye on your hunger and thirst if you're playing on survival). If you want to keep the Cuddlefish in the containment, make a save now. Once the egg has hatched, climb back into the containment using the hatch and pick up the Cuddlefish. Take it out of your base and drop it from your inventory, like you did with the egg.

The trophy will unlock as soon as you drop the hatched cuddlefish from your inventory.

Once you've released the Cuddlefish, you won't need it again, it's only use is as a pet.