Timing starts when "Game start" is selected and ends on final hit on last boss. The leaderboards are currently split across language differences - US versions of the game utilize a significantly slower damage table.
Wrong Warp rules: Timing starts when "Yes" is selected to load the save to set up the wrong warp, and ends on final hit on last boss after completing the wrong warp. For this category, after exiting the boss rush room, you must begin a game with the "Game Start" option. If you are beginning a NG+ save after setting up the glitch, please submit that run under Wrong Warp (NG+)