Extra high speed mode:
Press Up(2), Down(2), Left, Right, Left, Right, B, A on controller two at the title screen. Asaka will say "Excellent" to confirm correct code entry. "High Speed 3" may now be selected on the option screen.

Boss backgrounds:
Press L, R, L, R, L, R, A on controller two at the title screen. Select Vs. battle mode game and choose characters. The Metro Train and Studio 6 Stage will now be available on the stage selection screen.

Level select:
Press A, Y, A, Y, X, Y, B, A, R, L at the options screen.

Fight as Bosses:
Enable the "Extra high speed mode" code. Then press X, Up, Y, Left, B, Down, A, Right, X, Up on controller two at the title screen. A female voice will confirm correct code entry. Choose Vs. mode and move to the left of Shredder to select Rat King or Karai.

Use final attacks in Story Battle mode:
Press Up, Left, Down, Right, X, Y, B, A, X, Y, B, A, X on controller two at the title screen. The lower green bar for special moves will appear, just as in tournament mode.

Ten Turtles:
Press B(3), A(3), X(6) on controller two at the title screen. The sound of an explosion will confirm correct code entry.

Configure controller:
Press Select at the character selection screen.

Using Wingnut:
While you are facing an opponent you cannot defeat, use his dive bomb attack (Jump, Down + A). You should be able to defeat even Karai with this technique if you are fast enough.