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