Enter Tartarus alone or finish the battle with an All-Out Attack.
Enter Heaven's Door until you reach the tenth floor. Obviously, no one will be there since you did not accept the request. Go to the center of the room, then move slightly north until you see a prompt above the main character's head. Press X to start a conversation and Elizabeth/Theodore will suddenly appear. Accept the challenge to fight the ultimate opponent.
Reach the Top floor (252nd floor) of Tartarus and beat the Reaper.
Max out the "Nyx Annihilation Team" social link, then fuse Thanatos and Orpheus.
By clearing the game, you unlock New Game + In New Game + your current level, Persona Compendium, Equipment, Play Time, and Special Items you gained from Maxed Social Links are all carried over from your cleared game. In addition, you gain access to the Monad Block and an optional new boss is unlocked. NOTE: Consumable items do not carry over.
Die during a battle and do not use a Plume of Dusk. The introduction from the original Persona 3 will appear at the main menu.
Complete Margaret's Request. The Void Room will automatically open at 1/1.
To unlock the ultimate opponent you must clear Margaret's Request. Void Room will be automatically opened at 1/1. Clear it and Pandora's Door will open.
Complete the indicated task to unlock the corresponding Ultimate Persona.
Successfully initiate a fight, then run to the next enemy within three seconds or less. Even though you are in front of the enemy you will remain undetected. This trick is useful when trying to initiate a fight against rare monsters which can easily detect you.