Have lots of Jammin' Jellies, Ultra Mushrooms, and Life Mushrooms. Use Vivian whenever she does her really big blast. Otherwise you'll just have to use your mad skillz.
(I equipped Mario with a variety of badges that let me do quite a lot of damage every round; the jump badge that give more attack power to jump but takes away hammer, since you won't need the hammer. The badge that increases your combo damage but you do no damage if you don't get the combo; just always get the combo. Other attack and defense ups will also help, get rid of all the badges that are useless).