This is simple once you're at the end game (and you likely want to be at least level 70 to attempt it).
Activate the quest and it'll point you to each door which you must complete - if done in order then they get harder each time you encounter a new door (more floors to it).
Once you've done 9, you return to the quest giver and you then get to attempt the final dungeon.
However, if you're in hard mode, change to normal/easy now, as you can't get the trophy when in hard mode as the dungeon doesn't stop as expected, at floor 30. Beat the boss on floor 30, leave the dungeon and the trophy will unlock.