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.
Survive without breaking Mona's charge.
Defeat the Vampire Queen without letting her recover HP.
Defeat the Tentacle Monster without killing any tiny tentacles.
Una's direct damage exceeds 9999.
Lose on floor 20.
Unlock all CGs.
Reach the normal ending.
Reach the bad ending.
Lose on floor 100.
Kill 30 rare monsters.
All Una's abilities reach max level.
Reach the happy ending.
Win on floor 100.
Unlock all cards.
Obtain 170 Lv.3 runes.
Clear the succubus dungeon.
Win on floor 80.
Unlock 40 cards.
Trigger 10 trap events.
Kill 150 normal monsters.
Lose on floor 80.
Win on floor 60.
Unlock 20 cards.
Defeat Pamela while her clone is still present.
Lose on floor 60.
Trigger the slime trap.
Win on floor 40.
Lose on floor 40.
Trigger the spike trap.
Win on floor 20.
Trigger the chest trap.