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