Jump off the stage right before he dives in for the attack; he never follows you off stage.
Tabuu's butterfly ring/3 shock-wave/whatever-you-wanna-call-it attack has a timing to dodge depending on the level you're playing. Easy makes it slow, and Intense makes it so fast that you better not DARE to air-dodge or roll dodge.
I only know the timing of Intense. You better side-dodge, wait for like a quarter or half a second, side-dodge, wait for another half a second, then side-dodge. DO NOT ROLL DODGE OR AIR-DODGE. Roll dodge takes too long, and air dodging has too much time taken before using the next dodge.
Funny thing is that, the speed of that attack in Intense mood is so fast that Zelda can avoid it by transforming into Sheik (depending on how long your game takes for her to transform). Not sure about the PokeMon Trainer.