Hearthpwn

Simple deck for people who don't have much more than the Naxx cards. I'm guessing if you are doing this adventure that you at least have those.

Proof http://i.imgur.com/ek1EgGG.jpg (pretty lame proof but it's not exactly a hard achievement)

Mulligan

Anything except minions. You want to rely on his hero power to bring your minions out for you.

If your hand / Pile On! minions suck at start just concede and retry.

Strategy

Just look for a good opportunity to divine spirit / inner fire combo. Remember that he has execute. You will often get unlucky with him popping his taunt swarm / good minions while you get bad ones. Can't be helped really, just concede and try again if you have no chance. 

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If you find this useful please feel free to check my other decks for budget heroics. I post new ones as soon as I take down new bosses, and try to use as many budget cards as possible.

Please bear in mind that heroic bosses can often require a *lot* of retries before you will get the exact hand / play sequence you need to beat them. This is especially the case when attempting them on a budget. However, any deck I post for heroics I will only post when I have successfully used it to complete the boss, and consider it to have a reasonable chance to succeed again.