While playing as Bowser, you can grab the opponent with his special side attack (Left/Right + 1/B/b) and Bowser should jump up and do a midair flip with the foe. While he's doing this, you can move him off the stage in midair so he takes the foe off the stage with him, thus, you both loose a life. This is very effective when the opponent only has 1 life left, or when both of you are at your last life. (When both of you have 1 life and you do this, you'll still win, since the foe got KO'd first.) DO NOT DO THIS WHEN YOU HAVE ONE LIFE LEFT AND THE OPPONENT HAS MORE.
Only 1 person can hold a ledge at a time, so if someone is trying to get to a ledge on the edge of the stage, grab the ledge so they cant and watch them fall to their death.
Sonic's greatest power is his speed. Randomize his attacks when battle begins, then pull out some big guns when you get a very damaged enemy with you. Also, move quick after that Smash Ball to get your Chaos Emeralds. When you become Super Sonic, you may not exactly be Chuck Norris, but it'll get you by.