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