i beat the game today and i found that the core couldnt be harmed until after takin out the main body, i also had a tough time while he was healin like 6800 between each of my party's rounds, but this was because i was only in the 50's for levels and i didnt have kotr or omnislash or any level 4 limit breaks actually.By the way casting reflect doesnt prevent him from healin himself either,i tried that, as for the next boss, i didnt find that supernova was that much of a pain other than it takin so long,the trouble i had was again my levels and the fact that i couldnt remember wot was needed to change u back from a frog,i had vincent as a frog for virtually the whole fight and cloud for about half of it,so i had to use red xiii mostly on his own,another bit of advise would be to use haste which i didnt have.it took me about an hour or more to do both and has taken a decade to finally get round to finishin it off,i had been in the crater for years but never gone back to it.