At the menu screen quickly press Right, Down, Down-Right, Down, Down-Left, Left, Triangle. You should hear a "whack" sound and the Game Start" letters should turn red. Start a game or a versus match. A new menu should appear that allows you to play as any character. Note: The enemies have the same HP as in the game. Pick a bunny and you're easy pickings. Pick Zeiram and your near invulnerable.
At the menu screen hold left for several seconds, then quickly press Right, Circle, Triangle. You should hear a "whack" sound and the option letters should turn red. You can now enter options and select "Extra" mode where you and the enemies are energized and sped up!
At the main menu, rotate the joystick 360 degrees then press X, Square, Circle, Triangle. If done correctly you will hear a sound and Versus Mode will be available.
Thanks to Revolution reader Jason Sommerfeld!