Hearthpwn

This is the deck I used to beat  Heroic Drakkisath.

I chose Druid as they have access to some of the biggest class-specific minions. The focus of the deck is to try to X-for-one Drakkisath as much as possible since he gets two cards a turn and you only get one.

Cards I don't have but would have tried if I did

• Foe Reaper 4000: Drakk plays a decent number of 6-health minions, so this guy seems like he could really do work.
• Gruul: Might suck for this match, but I'd like to try it. Drakk likes to just go face so if you can survive a bit, Gruul could maybe get big enough to win the game for you if you can parade out enough taunts and other minions. 
• Onyxia: filling your usually mostly empty board with 1/1's seems like it would be good.
• Malorne: It's a big card. It once popped out of Sneed's and kicked butt when it did.

Cards that performed well

• Deathwing: Great reset if he gets a nasty board.
• Mekgineer Thermaplugg: Gives you little guys to push through some extra damage and/or help take out his higher health minions.
• Ironbark Protector: usually 2-for-1s, can hold off a lot of pain.
• Ancient of War: great in defense mode when he has a bit of a board. great in offense mode to take big chunks off his HP
• Kel'Thuzad: Super awesome as long as Drakk doesn't immediatly hit you with Twisting Nether
• Sneed's Old Shredder: Big minion that poops out another big minion when it dies.  Combos well with Deathwing
• Piloted Sky Golem: See above.
• Sunwalker: Pretty great speed-bump after you have a bit of a board.  Can keep you alive another turn while your big dudes beat face.
• Dr. Boom: Will ususally 2-for-1 and can 3-or-4-for-1 if the boom bots roll high and hit the right things.
• Alexstrasza: Chops off 35 HP.  That's a lot of HP.

Cards that didn't do as well as I thought they would

• Cairne Bloodhoof: Just didn't have the attack to actually kill anything.  The best attack for going against this deck is 7, 6 is okay and 5 or lower has trouble killing anything.
• Swipe: As above, 4 damage doesn't really cut it.
• Starfall: 5 damage could usually kill one thing, but not often enough, I never found myself in a position where the 2-damage option was any good.
• Ragnaros the Firelord: Only drew him in one game and he proceeded to hit Drakk's face instead of his minions 4 turns in a row.

Cards I haven't drawn yet

• Stormwind Champion: Might be better as another giant.
• Cenarius: Seems like he would be good.
• Troggzor the Earthinator: Drakk plays some spells, so he seems like He'd do work.
• Sludge Belcher: This was a late addition after I saw how well Sunwalker did.

Some cards I might try

• Big Game Hunter: Reasons I didn't try him: 1) Most of the time he would just 1-for-1 as 4 attack is rarely enough to kill one of Drakk's minions.  2) A lof of Drakk's minions have 6 attack, thus rendering BGH useless.
• Maexxna: Would probably usually 2-for-1, seems like a good option
• Illidan Stormrage: His 5 health is a problem, he probably wouldn't survive more than 1 attack to an enemy minion.  But, if you go face with him and he survives, you could get a few flames which might turn the tide.
• Rend Blackhand: I only ran 2 dragons in this deck, so I figured I wouldn't get his battlecry often enough. If I had Onyxia I would probably have given it a shot and maybe also thrown in Malygos, Swipe and Starfall.  Also maybe Azure drake?  I don't know if spellpower would be viable.  Maybe as a mage.
• War Golem: Most of the time a 7/7 will be able to get a 2-for-1.  If you are lighter on legendaries, more giants and war golems wouldn't be terrible.
• The Black Knight: This would probably actually be pretty good. Being able to get through his random taunts would probably be worth.