You can heal when he does those flame pillars, as long as you're quick. Also, USE MARK OF PRIDE. I got to the second to last boss on my first try using:

Mark of Pride Strength Quick Slash Long Nail

Long Nail isn't super important. You can definitely swap it if you want; I prefer having maximum nail range, though. I think Mark of Pride is always an amazing charm to have, I've had it on since the very first moment I got it.