After you've unlocked Nightmare Mode and Ultimate Mode, you'll automatically gain access to the Boss Rush, which gives you control of all four party members and a selection of their subweapons. Note that you can only equip one subweapon per character per fight, and Zangetsu doesn't have any of his special abilities from the Bad Ending route.
Nightmare Mode
After beating the game on Normal Mode, you'll unlock Nightmare Mode, which continues the story and gives you immediate access to all the characters except Zangetsu.
Ultimate Mode
Beat Normal Mode, but kill all of your companions instead of recruiting them.