That's Super Mario World: Super Mario Advance 2.
Anyway, you wait for him to throw Mechakoopas down. Then, you jump on the Mechakoopa, and grab it. Then, while holding up on the D-Pad, let go of B and time it so you hit Bowser. Also, it's a good idea to spin jump any Steelys (metal balls) that Bowser drops.
You can be silent and let the world think you are a fool, or you can open your mouth and remove all doubt.