On the Turtle Select Screen, press Down five times for a one-player game, or press Down 10 times for a two-player game. With this code, whenever you are defeated, the game will randomly select your next turtle. So, while you may start playing with Leo, after being defeated, you may continue with Don, Mike, or Raph.
Stage Select and Options
On the screen where the title of the game and the choice for number of players appears, press Up, Up, Down, Down, Left, Right, Left, Right, A, B, Start on Controller 1. Then select your turtle, and you'll go to the Options screen. If you're playing a two-player game, press Select before Start.