I agree, to a point, with LoDL about Eowyn. Although she's got the shield-maiden status going for her, her defeat of the Wikkie was almost a given.
1) she had the prophecy going for her. You can see my opinions on prophecies on
this thread.
2) she had a shield. He had a big scary mace, yes, and yeah, it broke her arm, but physically, all she did was stop it. She didn't counter it, she didn't take it from him per force, she just stopped it.
3) his main weapon was fear. Her fear for her uncle's life (or at least honorable death) simply over-powered her fear of the big scary jerk.
Sure, she's great. I'm not denying it. Heck, Eowyn's one of my favorite characters. But she's certainly not one of the best fighters. One of the most stubborn, sure; but one of the most careless as well. Being an emotional and slightly suicidal gal doesn't qualify you to rank with Aragorn, Gil-Galad, or those other guys for best fighter status.