Any character that have strong air attacks and can stay in the air long enough to avoid Tabuu's many attacks that hit along the ground should be good for fighting him. Be careful when using exceptionally light characters though, because they also die faster when being hit by these attacks.
In order to avoid the Off Waves attack, you need to spot dodge by holding the shield button and pressing down on the joystick.
You can view strategies for fighting Tabuu in these YouTube videos. I've listed the times when Off Waves happens, so you can see what timing you need to dodge the waves:
- SSBB: Final Stage Tabuu beaten by only Zelda SSE (Off Waves at 2:02 and 3:13)
- Super Smash Bros Brawl, Pit vs Tabuu on Intense mode (Off Waves at 1:24, 2:44, and 4:04)