Here is the full list of all 22 Lunistice achievements.
Get all S-Ranks in all levels as Toukie
Ruin the cat slimes' vacation
Collect all Baubles as Toukie
Beat the game as Toukie
Remove all crystals in Stage 3 - Act 1
Land on the big Jerry's head
Find all Box Buddies in all of Hana's levels
Collect all Stars as Toree
Get all S-Ranks in all levels as Toree
Beat the game as Toree
Collect all Cranes as Hana
Get all S-Ranks in all levels as Hana
They were kinda asking for it
End Lunistice
Beat Stage 7
Beat Stage 6
Beat Stage 5
Beat Stage 4
Bonk.
Beat Stage 3
Beat Stage 2
Beat Stage 1