Successfully complete the game to unlock New Game+ mode, which allows you to retain your previously obtained level, Persona Compendium, equipment, play time, and unlocks special items from Maxed Social Links. You will also have access to the Monad Block and an optional Boss.
Reach the 252nd floor of Tartarus, and defeat the Reaper. Heaven's Door will open automatically at 1/1.
Successfully complete Margaret's Request, and The Void Room will automatically open at 1/1.
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.