Hearthpwn

Use Coldlight Oracle (try to combo with Brann Bronzebeard and Gang Up) to fill the boss's hand up to 10 cards.  This stops the boss's hero power from creating 0 cost cards and can start to mill the boss, setting up for Vanish to destroy many tokens.

Use Mind Control Tech (try to combo with Brann Bronzebeard) to pray you steal his strong minions.  Getting lucky with MCT is a win condition.

Use Antique Healbot/Cult Apothecary (try to combo with Brann Bronzebeard) to stay alive.  Use Sap to stay alive and destroy cards (if boss's deck is full).  Use Deathlord to stall and stay alive and help deplete boss's deck.

Use Fan of Knives and Bloodmage Thalnos for card draw and to reduce his board size (sorry, you won't be clearing, usually just killing 1 to 3 minions).

Use Gang Up on Brann Bronzebeard and Coldlight Oracle to increase your chances of drawing the above combos and clogging his deck to stop his hero power.

Use Eater of Secrets to erase the boss secrets.  Often times you can hit 2 or 3 secrets in a single play.

Use Shadowstep to help replay any of your useful battlecry cards: Coldight, Secret Eater, Healing, MCT, etc.

Use Preparation to keep tempo going.  This is mostly an enabler for Fan of Knives so you don't stall out on cards, but can also help pull off an important Vanish/Sap/Assassinate.  Use Vanish and Sap to get rid of Ancestral Spirit minions.

If the boss hero power draws and plays a very large 0-cost minion during turns 1 through 3, just concede and start over.

Expect to play 10~30 games before you win.