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
They were kinda asking for it
Get all S-Ranks in all levels as Toree
Collect all Stars as Toree
Beat the game as Toree
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
Remove all crystals in Stage 3 - Act 1
Get all S-Ranks in all levels as Hana
End Lunistice
Collect all Cranes as Hana
Beat Stage 7
Beat Stage 5
Beat Stage 6
Beat Stage 4
Bonk.
Beat Stage 3
Beat Stage 1
Beat Stage 2