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