The idea here is to use Shade of Aran’s Hero Power which gives you +5 Spell Damage against him. You don’t want to attack with minions unless he doesn’t have a Secret up because eating 10 damage from Flame Wreath (Heroic) will likely make you lose to his damage spells. You will want to have some minions though, they absorb hits from the Arcane Missiles and can give you beneficial effects. Most of the cards are used for cycling through your deck to get to your burn, you could experiment with cards like Pyroblast, but it might be difficult to get to 10-mana. Cabalist's Tome is another card that could work in this deck.
Arcane Blast is really good at removing his pesky Avian Watcher.
Another card that might work is Animated Armor, this would help reduce the incoming damage from his spells, but doesn’t work great against Arcane Missiles.
Thanks, it worked like a charm 🙂