DukeWellington reminded me about Belegost with this comment:
Can we talk about Ruins of Belegost though. I mean for months we had so much complaining about Carn Dum, most of which I disagreed with, but Ruins of Belegost is clearly much harder and nobody says anything about it. I mean that quest is more difficult than like 75% of nightmare quests. Carn Dum was pretty easy by comparison.
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Now I do know that part of the reason is that Carn Dum is more difficult two handed and Belegost is hardest in solo, but even two handed it's rather brutal. I just never hear anything, so is this just me?
I'm primarily a two-handed solo player, and I had MUCH less trouble with Belegost than with Carn Dum. I thought that perhaps the deck pair I used to beat it, which is by no means quest-specific, might be informative for anyone struggling against the quest: http://ringsdb.com/fellowship/view/848/the-eagles-have-landed-in-belegost
Fuller details in the fellowship/deck descriptions, but the general idea is to use Support of the Eagles to boost up Tactics Boromir. Pumping those eagles out takes a lot of resources, but the natural Tactics/Leadership pairing falls short on card draw, so its companion deck uses the ol' Gandalf-Elrond-Splorfindel power trio to get out an Eagles of the Misty Mountains as quickly as possible.
While I haven't actually tried, I don't think this fellowship would have a chance against Carn Dum -- for offbeat personal reasons, there's a dearth of shadow cancellation in these decks. But it should work pretty well for more normal quests. Check it out! Support your local eagles, and they will support you in return!