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