As Eowyn, I have found it very difficult to defeat the Witchking. I myself have only done it two or three times. Here is one way to defeat him.Defeat the Witchking's fell beast, and then the Witchking will dismount. Run away from him. Keep running and he will chase you. Go to the top of the screen. The Witchking will follow you. There is about a 1/20 chance that the game will glitch at that point, and the Witchking will get stuck, and will start running around in circles. At this point, he will not even be able to hurt you, and you can just run up to him and slash him until he is defeated.(It helps if you have the power that makes you able to run really fast.)