After completing all 67 substories and every Battle Dungeon mission, go to the Battle Dungeon reception to trigger an event (triggered automatically after completing the final battle dungeon mission, if you have already completed the substories). The receptionist tells Ryoma of a man with great skill and wants Ryoma to help deal with him.
When you are ready, select the final battle dungeon mission (20: Defeat Toyotomi Hidebu). When you enter the room where you faught Toyotomi, an event is triggered and you fight Amon Genjuusai.
After defeating him, leave the Shinsengumi HQ area, then return and go to the reception and Ryoma will be told about a challenge to a fight from Amon.
Go to Kiyomizudera and fight Amon Genjuusai again.
This fight is no joke. This is the hardest fight in the game, so come prepared (plenty of healing items, etc). It is actually possible to disarm him (using the sword style, R1+Circle counter), so you can make your life a lot easier by taking away his sword.
After defeating him you get the Enchanted Sword that Time Forgot weapon.