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