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