Here is the full list of all 33 Castle in The Clouds DX achievements.
Clear without taking the heart
Use fighter after clearing
Use thief after clearing
Bad, good, best, see all three endings
Got all the treasure
Got a treasure
Lost treasure
Make map reach 100%
Defeat the core
Defeat the Ancient queen
Take all the hearts
Own all weapons
Got Excalibur.
Level 200
Got all abilities
Defeat the death
Defeat the Lamia
Level 100
Defeat the succubus
Defeat the dragon
Defeat the 1000th enemy
Defeat the pirate queen
Level 50
Defeat the Ice Queen
Defeat the Scylla
Defeat the 500th enemy
Defeat the Poltergeist
Defeat the bandits
Defeat the 200th enemy
Got the first ability
Take the first heart
Level up for the first time
Defeat the first enemy