To unlock this, all you have to do is the following:
Open up all Chest
Unlock every room
Fight Yarlanda 4 times
(One in each Dungeon location, top 3 Dungeons, and one in the Marketplace. Marketplace should be last)
If you do everything before the Fourth Dungeon you should unlock this right before you save the Professor
Note: You dont need to buy any armor, weapons or upgrade anything to unlock the achievement.
Good luck.