Step By Step Requirements:
1: New Game Plus is required. Cannot be accessed on a first run.
2: The Empress social link must be completed. Margaret's request need to be completed in the run you wish to fight her in.
3: Every optional boss in each dungeon must be defeated every time you clear a dungeon a new shadow appears at the top. You need to defeat every single one.
4: You need to be going for the True Ending by March 30.
5: When Igor gifts the Orb of Sight item, go back into the Velvet Room. Margaret should give you a secret request.
6: Climb the Heaven dungeon again. Once you reach the top, you can fight the hardest challenge in the game.