Hearthpwn

This is the deck I used to beat Heroic Lord Slitherspear. After trying a few mill Rogue and other miscellaneous decks, I went back to the old tried and true OTK Priest.

This is a pretty cheap list, Big Game Hunter probably being the real expense, and likely not necessary.

The idea is to obviously get Northshire Cleric or Deathlord out as soon as possible (turn 1-3), then buffed with Divine Spirits, Inner Fires and Velen's Chosens. You should ultimately shoot for a 20/20 minions, or better. Go face and ignore the board (unless a trade really really makes sense...like kill one minion in the early buff phase to gain control. If any taunts, buffed cards or freezing minions get in your way, use one of more the many silences in the deck. Try to hold Mass Dispel to get good value, and hit at least 3+ minions.

Keep you minion healed always with Circle of Healing and hero power.

Honestly, if you get the draw the game should be over by turn 5-7. if you run into problems there is removal:

Pint-Sized Potion + Shadow Word: Horror to wipe an entire board or 5hp or less minions.

Auchenai Soulpriest + Circle of Healing can clear a board of 4hp or less minions. But if possible save Circle for you buffed minion.

Also single target removal with SW:Pain, Death, BGH and Giant Wasp.

In reality though, if you get bogged down with needing the removal you're probably behind and should just restart.