Alright, so I figure we might as well do something dumb with Passage Through Mirkwood for the inaugural Quest of the Week, and McDog and Durin's Father have already got some fun ideas for how to beat the quest in just one round, so I figured I should try to beat it with just one character.
The history of the overpowered Mono-Thalin deck is well documented in LotR LCG lore, but not published in many places. Seastan has a fun one using Forth, The Three Hunters! that you can see here. So I figured I'd use the more obvious The Grey Wanderer contract to try it out so as to not have to kill off a couple of innocent bystanders.
The deck can absolutely still lose to the quest, and I did a couple of times, so it isn't fool proof, but the idea is pretty sound. You really need Song of Kings, Steward of Gondor or In Service of the Steward and Gondorian Fire and then you can use either Grappling Hook or Trained for War to Battle quest through each of the three quest stages once you have enough resources stacked up. Fire also serves as the easiest way to kill Ungoliant Spawn if that is the path that you get for the random Stage 3.
It has enough other tricks with Strength and Courage, readying from The Ring of Power, Bilbo's Plan, etc that I found I was able to limp my way through the opening few rounds for long enough to draw into my combos. Typically Strider is the best GW attachment, since you can dig with An Unexpected Party for your Song of Kings more easily than if I flipped the card counts around, and having the option to Strength and Courage that opening Forest Spider on turn one is a good way to get some breathing room on the questing so your threat doesn't skyrocket to quickly while you underquest each round getting set up.