Because tips for this battle are hard to find (most FAQs focus only on Shanoa mode) and this took a stupid number of tries, my suggestions to anyone else trying this:
1. Grind up to level 25 if you're not there yet. I was at 22 when I started this and getting nowhere. This makes a big difference, because:
2. When you first enter the boss fight room, if you do enough damage quickly enough, he will disappear without attacking. So if you've leveled up enough, jump when you enter the room and use your rapid-fire gun on him, and he should spazz out and disappear without doing anything.
3. You can *repeat* that several times once you know the timing. Don't chase him after he disappears - wait a moment, then fire off a Max Shot to the right. He'll start to come onto the screen and get hit by it. Jump and rapid-shoot him again and he should, once again, disappear. As long as you can hold this pattern you can get in damage to him at no danger to yourself.
4. Eventually he will manage to attack, and obviously each attack has its own pattern to dodge. For the Fire attack I found that running a little ways to the side, then double jumping into the air and warping the other direction is an easy and repeatable way to avoid all the fireballs. Step left, hop hop, warp right, hop hop, warp left, etc. The Ice attack you have to stay off the ground, and the Globus attack, if you time it right you can use the invincibility aspect of the flame-kick.
5. Stay on the left side of the room; if you ever get away from it run/warp back there fast. Because if he ever does his Electrical Cage attack, you must warp to the far right of the room and duck in the corner until he's done - and this only works if he started his cage move by moving to the right. Which he'll do if he was on the left side of the room. If he starts electrifying on the right, you're screwed.
6. When you get him down enough to start using the rush attacks, invincible fire kicks all over the place should protect you.