When playing the Piranha Challenge, choose a character that is fast and/or tall. (i.e. Luigi, Waluigi...) When the game starts, immediately run up to the net and stay there. If your character is tall enough, he/she will be able to return any ball, even ones with an orange trail. But what about the opponent, you say? Well, here's the trick. Whenever a ball is shot, return it toward the piranha plant that shot it, so if the left one shoots a ball, return it to the left. If you keep this up, the opponent will become confused and won't be able to return a single shot you make. But careful: you've got to be quick!
(NOTE: If you're having trouble reaching the ball, look at the piranha plants. Just before they shoot, they cock their heads in the direction they're going to shoot. This should give you a good head start.)