To be invincible, start a two player game, when one of the characters used run out of life points and their death animation begins, have the other player press the start button. (If player 1 dies, player 2 should press start or vice versa.) Then have the player choose that character again, the character will then be alive but have no life points, and thus be invincible.
Round Select
To select any round, hold down A + C + Start during play, then reset the console.