This is an updated version of the original deck I used to defeat all of the quests of campaign 1. You can see it in action here.
The main idea behind this deck is using two ranged heroes, Faramir and Legolas, to essentially render guard meaningless for Sauron. The allies are all very low cost, either 1 or 2, with the exception of a single copy of Gandalf. This allows you to get them out quickly, and most of them have an arrival effect of some kind (which you can get added value out of with Borne Aloft). Since I'm not using Arwen, I've included plenty of healing with Lembas, Self-Preservation, and Beorn's Hospitality. A key attachment is Unexpected Courage, especially for Eowyn, while the rest of the attachments can go on the fighters. Overall, this is a very well-balanced deck that should give you a chance at a perfect score.