This deck is particular built for The Waste of Eriador solo play. It's a thematic deck where Eowyn and Merry ride together, and I don't want to use Boromir, Gandalf, Elrond or other over-powered decks which become boring after many plays.
At the beginning of the game, you need lots of card draws and might want to mulligan for Ancient Mathom and/or use Dwarven Tomb to reuse it. Use Éowyn's card discard power and Stand and Fight to bring in Warden of Healing and Gléowine early in the game.
The key attacker is Dúnhere. You want to equip him with 2 Spear of the Mark as soon as possible so he gets 7-attack against enemies in the staging area. Most enemies have less than 7 defense+HP, so each blowfrom Dúnhere will usually take care of one enemy. Then equip him with Unexpected Courage and you are pretty all set with battles. Equip Herugrim and Snowmane to Éowyn. But that's mostly to help fight the final boss where Dúnhere cannot kill with one hit.
Merry and Hobbit Pony are pretty handy to keep threat under control. The second copy of Unexpected Courage should go to the hobbit. Elfhelm is a natural fit to the first stage as he can reduce the 1 threat when it becomes night. Gamling will take care of recycling Rohan allies during stage 2. Most of the time is likely to spend on stage 1. By the time you are at stage 2, you should be able to get Gamling with the help of Mustering the Rohirrim.
You might also experiment with cards in the Sideboard. Silver Lamp and Small Target are fun to play, but they need too many card slots, and the scenario has lots of shadow effects and Small Target hardly applies.
Wasn't able to make it work : the quest is so punishing for solo play with the 3 encounters in two rounds... Needed Elrond on a deck I found on cardgamedb... I do like your build though : I never used Elfhelm before but he clearly is the man of the situation here.