This is an easy deck to beat Drakkisath with, relying on the poor AI of the boss. When you have Kel'Thuzad and a Taunt minion out, Drakkisath will NOT attack the taunt minion for any reason. Drakkisath will still use Kidnappers and Flamestrikes on Taunt minions, so be sure to get more than 1 Taunt minion out quickly! Keeping Kel alive is the priority, as well as defeating Drakkisath before he uses Twisting Nether.
However, Drakkisath has a few ways to kill Kel'Thuzad, so the goal of this deck is to get Kel'Thuzad out and keep Kel stealthed to protect him. Use your other minions to hit face and win while Drakkisath does nothing.
Beware, this deck is very dependent on Drakkisath's first turn. Ideally you will play Kel on the first turn, but if Drakkisath immediately destroys him, it's game over. Simply restart and try again. Once you get Kel stealthed with Master of Disguise, Drakkisath cannot use his "destroy a minion - gain 10 armor" spell on Kel. You have to still be wary of double Flamestrike and Twisting Nether.
To limit the risk of Flamestrike, swapping in a couple Earthen Ring Farseers might be a good idea to heal Kel after a single Flamestrike. There is no way to avoid Twisting Nether with this deck. You just have to get lucky and hope Drakkisath doesn't draw it. One thing I've noticed and a couple other people have mentioned - if Drakkisath has a board full of his own minions, he won't use Twisting Nether (or use it much less often).
Be careful when using Conceal. Use if BEFORE attacking with your Taunt minions so they lose Stealth on Drakkisath's turn.
Also, you can replace many of the cards in this deck. Sylvanas gives an insane amount of value, but once you get a stealthed Kel + Taunt, you don't *need* anything else to win. So use your good legends if you have them, but Kel and the stealth cards are the only essentials in this deck. Alexstrasza is very useful if you have her.
Here is a video of the deck in action, courtesy of Matt_Sparks.
Swapped Loatheb for a Core Hound after being notified that Loatheb's Battlecry has no effect. Drakkisath's hero power overrides it. All cards cost 1, and not a thing can change that.