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