After Bowser is "defeated", Mario jumps on some platforms and enters another part of the course where you need to avoid fireballs coming out from the walls while Bowser swings at the platform you are standing on. To avoid being knocked into the lava, I recvomend waiting until his eyes change color and then jump to another platform that isn't in the same vertical position. I strongly reccomend using a Super Leaf and keeping one in storage on this part of the course! Also you can wall jump over Bowser before this section in the first battle easily with the Super Leaf. I hope this helps.