if for some reason you have every adventure available, yet have not completed any mission, Astral Druid seems to currently be the best deck, where it works in most missions.

Astral Druid involves having a copy of innervate and a copy of astral communion in your deck and restarting the mission until you have both of them in your hand. The rest of the deck is ultra high cost cards (especially card generating ones) and card draw, Such as Ysera, The Lich King, Yshaarj, Ultimate Infestation, Nourish, Rafaam, and others

Astral Druid is able to work against Most Heroic bosses which otherwise require specific decks in order to beat them. I have personally tested by using Astral Druid to beat every single mission

There are currently 66 Missions, or 61 where you need to bring your own deck. Of those, Astral Druid is able to beat all the missions on Heroic (Definitely, I did it myself) EXCEPT FOR

Naxxaramas - Maexxna

Gluth

Sapphiron

Blackrock Mountain - BY THE POWER OF RAGNAROS

Baron Geddon

Highlord Omokk

General Drakkisath

League Of Explorers - The Steel Sentinel

Arch Thief Rafaam (well you know why)

Honorable mention: Chieftain Scarvash (Had to start with 2 Innervates and astral)

Icecrown - Deathbringer Saurfang (Unless you get two Frostmournes from The Lich King)

Lady Deathwhisper

Note: Blood Queen Lanathel requires you to get two innervates astral immeditely, or run Forbidden Ancient, etc

Including Scarvash, we can see that we can beat 49 out of 61 of Heroic missions which require us to bring our own deck, or more than 80%, and these missions usually require you to build a specific deck for them. Pretty good I would say