Enter these 20-character passwords by selecting Continue from the title screen.
After you beat all 7 opponents and the "END" screen is displayed, hold Up + A on the second controller, then press any button on the first controller. Instead of the regular title screen, you'll get to the secret opponent challenge request. Press Start then select the "VS MODE" to play it. (Note: the Password 66666666666666666664 also gives you this fight.)