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 kin. Begone, if you be not deathless! For living or dark undead, I will smite you, if you touch him.
Éowyn is Boss Hoss Applesauce, and even the Nazgûl have cause to fear her. This deck is a questing powerhouse that relies on getting the shield-maiden her adoptive father's sword and letting her wail on any enemies foolish enough to engage.
Everything except the Harp goes on Éowyn. Herugrim is only good for one attack, so don't go crazy with the Unexpected Courages unless you plan on defending with Blood of Númenor, too. Obviously try to limit yourself to engaging one nasty a turn if possible.
Arwen and Elven-light are the engine that get the deck going, so mulligan if you don't have one of the latter in your opening hand. Éowyn can help discard them, speeding up the draw further.
All spare resources go on Éowyn. Let Arwen pay for spirit cards when possible, use Envoy of Pelargir, Errand-rider, and Miruvor to shift resources over, and dump every one of Théodred's bonus resources on her, too. When she's groaning under the weight of her wealth, use a Lay of Nimrodel to either roll over a nasty quest stage or one-shot a nasty enemy.
If you don't need one massive hit like that, consider using that huge resource pool to pull a beefy ally out of someone's discard pile with Stand and Fight. This is a good way to get Faramir into play if Théodred is low on Leadership resources, too.