I just remembered that I had a [censored] of a fight with a Hagraven when going after the sap for the tree in Whiterun. The Hagraven was blasting me with great accuracy from a distance with a firebolt spell and when I got in close her claws were deadly. I ended up running in a continuous circle around her slicing at her while flaming her with the flame spell, she went down and my health was extremely low. That was tough.
I managed to beat her by just running straight up to where she was and killing her. At close range she doesn't use magic, so just run up immediatly and victory is yours.