Here is the full list of all 19 LAY achievements.
Restore energy to Nymphea island
Restore energy to Reimya island
Restore energy to Mont Hazetis island
Restore energy to Windrose island
Finish game
Gather all the magic crystals
Fly for some time (2 min)
Don't move for some time
Don't move in the air for some time
Fly by yourself for the first time
Get caught falling by the stingray
Make a bernardo fly away
Get yourself overloaded
Throw a fruit
Press spacebar
Throw a fruit in water
Land on Nymphea island
Get your lightning stolen by a bernardo
Try to fly away from Lay