The easiest way is to look for a Fire Shield. There's one near the start of the level if you stay in the middle hight of the lava falls, and a few others scattered through the level. With a fire shield he can't hurt you at all.
Without a fire shield, I suggest you to stay on the right side of the arena, wait for the fire to reach you then leap above it as you go to the left. Hit a pipe when you can. If you time it right, you should be able land a hit and have the fire dissipate before it can reach you on the other side.
Good luck!