Originally Posted by EvilMike

This is correct. It's an annoying jj2 bug, and makes the boss health bar completely useless, but the boss IS possible. Make sure you use the carrots. And if you have any powerups, use them. Another tactic you can use, if you are bad at stomp-blocking the fireballs, is intentionally get hit by the boss itself instead of the fireballs. This way you will lose 1 heart instead of 2, and greatly extend your life even though you are taking a lot of damage.

Of course, I should say that if you play it in hard mode, you probably would disagree with me. But even then, it's theoretically possible.