Éowyn is described to be very beautiful; she was tall, slim, pale, and graceful, with long golden hair and grey eyes. In temperament she was idealistic, spirited, brave, high-minded, and lonely.
During the battle of the Pelennor Fields, she confronted the Witch-king of Angmar, Lord of the Nazgûl, after Théoden was injured. The Witch-king threatened to "bear [her] away to the houses of lamentation, beyond all darkness, where [her] flesh shall be devoured, and [her] shriveled mind be left naked to the Lidless Eye." The Witch-king further boasted that "[n]o living man may hinder me," referring to the 1,000-year-old prophecy by the Elf-lord Glorfindel, foretelling that the Witch-king would not fall "by the hand of man". Éowyn then removed her helmet and declared:
"But no living man am I! You look upon a woman. Éowyn I am, Éomund’s daughter. You stand between me and my lord and king. Begone, if you be not deathless! For living or dark undead, I will smite you, if you touch him." - Wikipedia on Eowyn
I have to give it up to Tolkein . . . yes Frodo and Samwise save the whole world, but it is a lady who brings the enemy down in battle. To me Eowyn is the epitome between hard and soft. She is lonely and wants love, but is also a skilled warrior willing to run straight to battle. I kind of adore her.