You can't damage Bellegar directly in that fight, I found that simply killing off his summons (it seems that at any time one of them has a special aura about him/it) resulted in his own health being reduced and that even when I did randomly target him I was never able to actually inflict damage on him (Bellegar) himself.
Just kill off his cronies, basically.
edit: to the original poster - are you sure you got them in the right spots? One of the clues is actually a negative, though a fellow member seems to have listed the correct order above.
there is a big gate inside that dungeon, anyone know how open it?
Which gate are you referring to? Inside the actual vault or the champion academy?
