I haven't played this game much, but I think you have to let the others wreck each other, getting involved as little as possible until the end.
You can't possibly wreck more than one other car without wrecking yours. It doesn't matter if you hit or get hit, the damage seems to be the same. And when you hit another car's side with your front, it looks good but you're doing him a favor, since the front is always the first to go, and the side hardly ever gets hit.