Here is the full list of all 13 Fantasy Friends: Under The Sea achievements.
Use an involution potion.
Unlock all achievements!
Get all skins.
Get a show of affection from your pet!
Play All Unique Interactions.
Find a treasure!
Interact with a decorative object in the plaza.
Get all 12 pets!
Get your first skin.
Cure a pet
Complete the tutorial.
Evolve your first pet.
A new creature is born!