Combo Fellowship: Beat any Quest on the First Turn
Play a bunch of doomed cards to raise your threat above 40.
Trigger the Valor action on Rallying Cry.
Player 1 plays Dunedain Pathfinder over and over, to empty the deck of locations. He can be recurred with Born Aloft, which can be recurred with Second Breakfast. If you ever whiff, the Pathfinder will just come back to your hand thanks to Rallying Cry.
Player 2 then starts playing as many Pathfinders as he can. Every time he plays a Pathfinder, he gets to trigger Lord of Morthond to draw a card, even if the Pathfinder whiffs. Once the deck starts thinning out of locations, the Pathfinder will whiff frequently, meaning that player 2 will get to draw many times before the Pathfinder finds a location and stays in play. This makes the process of drawing into more Pathfinders or Born Alofts very easy.
Once all the (non-unique) locations are removed from the encounter deck, Player 2 can draw a card for free whenever he wants by playing a Pathfinder, triggering Lord of Morthond, and having the Pathfinder bounce back into his hand thanks to Rallying Cry. With infinite free card draw, it is possible to generate infinite resources using the loop described here: http://ringsdb.com/fellowship/view/4619/95-token-black-gate-or-beat-any-other-quest-on-turn-1
Once you have infinite resources, you can infinitely recur any event and beat pretty much any quest in the game in one turn. You can recur events like Ravens of the Mountain to place progress, kill any boss by recurring Durin's Song, reduce threat by any amount with Needful to Know, heal any damage with Lore of Imladris, kill any enemy in play with A Light in the Dark/Hail of Stones/Grim Resolve etc. Some more information on how to beat each scenario once you have infinite resources can be found here: https://hallofbeorn.wordpress.com/2017/07/04/deck-solo-first-turn-win/
For quests that absolutely force you to take multiple rounds (like Helm's Deep) you of course cannot have both players play Justice Shall Be Done on the first turn. This can make things trickier, but what you can do is have the second player pass his copy of Justice to the first player using Message from Elrond. That way you should still have enough resources to set up the combo on turn 1. These 1x cards can be found pretty easily with Heed the Dream.
I tested this on the Hills of Emyn Muil, which has more locations in the encounter deck than any other quest, at 20. I was able to remove all 20 locations on the first turn, use the combo to generate infinite resources, then play The Evening Star over and over until I had 20 victory points, then I played Ravens of the Mountain to get the 1 needed progress to win.
The fellowship could probably use a bit more optimization, but at the moment it works.