The idea is to use Éowyn to discard Beorn, bring him back with Stand and Fight, and use Ever Vigilant to have him block and attack in the same round. Beorn can take a hit from a Hill Troll, and when he attacks you can use his ability to do 5 damage to a Troll which often finishes it off if Gandalf already blasted it once. Once Beorn gets shuffled back into your deck after using his ability, if he is drawn again you can rinse and repeat, using Dwarven Tomb to bring Stand and Fight back to hand if necessary. Obviously it helps immensely to have Steward of Gondor early to pull off these combos (Steward goes on Eowyn). If you don't draw Beorn, Stand and Fight also works well with Gandalf or Longbeard Orcslayer (if there are at least 3-4 Orcs on the table).
I will often use Dwarven Tomb to grab A Test of Will from the Discard Pile if I don't have one on hand, as some of the treacheries are painful and deadly to Eowyn. There's a lot of extra staging in this quest as well as some surging, and Denethor can't look at everything. Both copies of Unexpected Courage are intended for Denethor to use his ability to control what comes off of the Encounter Deck, or defend multiple attackers. If needed can use Gandalf to lower Threat if I get too close to 35 (35 Threat triggers nasty effects of some treacheries). I have Faramir but never seem to draw him. Valiant Sacrifice, Lorien's Wealth and Gleowine are for more card draw. It might make more sense to pull Valiant Sacrifice and add a third Gleowine.
The deck starts slowly but usually gets rolling by Round 3. In one game I won in Round 5 despite not drawing a Steward of Gondor until Round 3 and drawing back to back Pursued by Shadow in Round 4 that raised my threat by 8. The deck can still get sunk by an unfavorable encounter deck opening draw such as multiple surges or back to back Locations that can lock you up and/or jump your threat quickly.
Note: since I am physically limited by having purchased only two core sets (I don't play online), there are only 2 copies of Unexpected Courage. If I had a third copy I'd use it in place of Valiant Sacrifice.