This thread will most likely be of greater interest to newer players, less so for veterans.
A few months ago, I defeated all of the Core/Mirkwood quests using the following pair of decks 2-handed. The decks are built using only cards available in the Core set and Mirkwood cycle (I own 2 Core sets and also bought additional Core player cards through e-Bay… you can always copy/proxy the relevant cards if you don't want to buy them). Beating all 9 of these quests with the same 2 "Core/Mirkwood only" decks can be a real challenge, given the specific deck-building challenges presented by each quest.
I've had the following success ratio with the decks when playing solo two-handed (all games played in standard mode):
Passage Through Mirkwood: 1/1
Journey Along the Anduin: 1/1
Escape from Dol Guldur: 1/4 (Thalin was randomly selected prisoner in the successful game)
The Hunt for Gollum: 1/1
Conflict at the Carrock: 1/1
Journey to Rhosgobel: 1/3
The Hills of Emyn Muil: 1/1
The Dead Marshes: 1/1
Return to Mirkwood: 1/3
DECK 1
Heroes