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