Here is the full list of all 13 月之泪 ～ Tears of Luna achievements.
Clear Normal difficulty
Clear Hard difficulty
Clear Lunatic difficulty
Clear BossRush
Pass Normal without continue
Pass Hard without continue
Pass Lunatic without continue
Clear BossRush without damage
Pass through stage 1
Pass through stage 2
Pass through stage 3
Achieve ending 1
Achieve ending 2