I've not played the DS version, but assuming he's the same as the N64 one, try standing right on the edge of the platform as far away from him as you can get. His shockwave attack is easy enough to jump over, and when he charges, you can backflip over him.
Now he's teetering on the edge, grab his tail. If you're at an edge by a bomb, you can just swing him into it, otherwise swing him around and take your best shot. This can be hard to get the hang of, but keep trying and you'll get the hang of it. (if you really want to get some practise in, try going back to the first Bowser stage and throwing him all over the place, as long as you avoid the bombs, you can keep practising until you've got it down.)
After the second time, he'll smash chunks of the arena away, so wait in the center until he's done, then find the furthest point away from him on the star, and repeat. Since you can't wait by a bomb anymore, you'll have to throw him. One more hit, and end of Bowser.
