You basically whittle his armor down slowly with your Hero Power, leave the Dragon Egg alone (he doesn't have anything to target them that would be detrimental - he kills them with his alchemist most of the time), destroy his minions early game, Vanish his in-game minions to burn his deck, and pretty much destroy his weapon with Acidic Swamp Ooze every turn.
Coldlight Oracle - Don't play this card early, unless you are really hurting for a specific combo. Mainly save this card at the end to finish him off with Fatigue or after you've played Vanish.
Azure Drake Mainly used for card draw and to trade with his other minions early on. Possibly replace one or both. If you have a Harrison Jones, definitely put him in for one of the Drakes or a Sprint (I don't have the card unfortunately)