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