To unlock the dressing room, you do not have to have beaten any quests at all, you do not have to have cleared the game on any difficulty. All you need is have at least 10,000 Meseta in your inventory.
If you have 10,000 Meseta in the bank and less than 10,000 Meseta in your inventory, you can't get to the dressing room, but if you have 10,000 meseta in your inventory, you can.
If you have 10,000 Meseta in your inventory, you can access the dressing room from the menu that comes up when you select your character from the character select screen. You go to "Dressing Room", and it says, "It will cost 10,000 meseta to make this change, is this OK?" and then you select OK.