Hint: Defeating The Basilisk
Have the selected spell as Inciendio. This should do more damage than Flipendo. When you enter the chamber, Fawks should "take" his eyes, making him blind. When he goes in a circle, continuously cast Inciendio. Make sure he does not touch you, or you will be poisoned. Watch out when he makes rocks come down and dodge his spit. This may take awhile, but you will eventually defeat him.