Here is the full list of all 33 Take Me To The Dungeon!! achievements.
Unlock all cards.
All Una's abilities reach max level.
Reach the normal ending.
Obtain 170 Lv.3 runes.
Clear the succubus dungeon.
Unlock 40 cards.
Kill 30 rare monsters.
Win on floor 80.
Win on floor 60.
Lose on floor 60.
Win on floor 40.
Kill 150 normal monsters.
Lose on floor 40.
Unlock 20 cards.
Win on floor 20.
Lose on floor 20.
Defeat the Tentacle Monster without killing any tiny tentacles.
Trigger the spike trap.
Trigger the chest trap.
Lose on floor 80.
Win on floor 100.
Lose on floor 100.
Trigger the slime trap.
Unlock all CGs.
Reach the bad ending.
Reach the happy ending.
Trigger 10 trap events.
Defeat the Vampire Queen without letting her recover HP.
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.