Normally, the game doesn't allow more than one player (most likely due to a glitch in the programming), but there's actually a way to bypass this in 1P vs. CPU mode.
In the Player Select screen, choose to play as any character (1P) EXCEPT Hothead. Next, the game will ask you to select your opponent (CPU) and here is where you choose Hothead. Now play the game normally, it doesn't matter whether you win or lose.
When the match is over, go for a rematch. This time, choose Hothead to be your character. The game will once again ask you for your opponent, but look and behold! The CPU cursor is already on Hothead. Choose him and enjoy the forbidden battle (unfortunately there doesn't seem to be a way to do this with a 2nd player).
During Story or Vs. CPU modes, the second player can skip to to the Vs. Player mode's player selection screen by pressing Start on their controller. This will not work during Story Mode's Bonus Game, however; to make it work during this section, you must press Up, A, and B together on Controller 2.