I use Ice Flowers to cut his defense and then Red Shells. When he falls down, I start stomping on him with Trampolines or Copy Flowers.
When he gets huge and makes that UFO appear, it WILL kill you in the number of turns displayed, but you can knock the number back by deflecting one of Shrooboid's spiked balls at it--Mario will send the ball diagonally to hit it when it's above Shrooboid, Luigi will send it straight up to hit it when it's above you. And just keep icing him to keep his defense down and pummel him with whatever seems to do the most damage for you.