Drakkisath’s hero power is to make every card cost 1 mana, and to cap your mana at 1 and his at 2. That means, he can play 2 cards every turn, and you can play one. I experimented with a variety of ways to increase my mana or decrease the cost of cards past 1, but they don’t work. Basically, you just try and throw down the most and biggest (legendary) minions you have. Here’s my Druid deck (for the taunts):

  • Poison Seeds
  • Big Game Hunter x 2
  • Psych-o-Tron x 2
  • Sludge Belcher x 2
  • Cairne Bloodhoof
  • Dark Arakkoa x 2
  • Illidan Stormrage
  • Moonglade Portal x 2
  • Reno Jackson
  • Sylvanas Windrunner
  • Chromaggus
  • Ironbark Protector x 2
  • Kel’Thuzad
  • Ragnaros the Firelord
  • Sneed’s Old Shredder
  • Alexstrasza
  • Arch-Tief Rafaam
  • North Sea Kraken x 2
  • Volcanic Lumberer x 2
  • C’Thun
  • Deathwing
  • N’Zoth, the Corruptor

I don’t think there is another way to win this match, it’s a bit of sheer luck. In my winning game:

  • He used Twisting Nether on a single minion on turn one (I forgot who it was, but it wasn’t a useful one)
  • He returned my Deathwing to my hand so I was able to cast it twice
  • I got a Sylvanas from my Moonglade Portal near the beginning of the game
  • He had a couple of turns where he only played a single card (spell). I guess he had multiple flame strikes or something?
  • Was able to keep my health up so I didn’t have to deal with the 9/9s

I think this boss is really about how many Legendaries you have.