Here is the full list of all 33 Take Me To The Dungeon!! achievements.
Reach the normal ending.
Una's direct damage exceeds 9999.
Fight to the last moment with Mona while discarding all your cards (excluding item cards).
Unlock all CGs.
Reach the bad ending.
Lose on floor 100.
Defeat the Vampire Queen without letting her recover HP.
Trigger 10 trap events.
Unlock all cards.
Unlock 40 cards.
All Una's abilities reach max level.
Reach the happy ending.
Win on floor 100.
Obtain 170 Lv.3 runes.
Clear the succubus dungeon.
Clear the succubus dungeon while Una has maximum marks.
Kill 30 rare monsters.
Lose on floor 80.
Kill 150 normal monsters.
Win on floor 80.
Survive without breaking Mona's charge.
Win on floor 60.
Defeat Pamela while her clone is still present.
Lose on floor 60.
Win on floor 40.
Unlock 20 cards.
Lose on floor 40.
Win on floor 20.
Defeat the Tentacle Monster without killing any tiny tentacles.
Lose on floor 20.
Trigger the chest trap.
Trigger the slime trap.
Trigger the spike trap.