How do you beat the fire demon on the Devil May Cry 4

To defeat Berial, the demon acting as Captain of the Demon Army as Dante, there is no trick to it. All you need to do is keep cutting away at him and jumping to hit his head until his flames go out. Then, hit him with the longest most powerful combos you have. The principle is the same with Nero. Do the same thing, except instead of jumping, use the Devil Bringer to pull yourself up to his head