After getting the four hidden characters and the last boss, use these characters to finish the game once each, then a new option will show up to allow you to play the Big Head Mode.

To play as the final boss, set the Game Level to Difficult, Number of Rounds to 2 or higher, then finish the 1P game.

To play as Jacky, Sara, Bun Bun and Jeffry, set the Game Level to Normal or higher, then use each character to beat the game.