Hearthpwn

Avalanchan's deck consists of mostly Molten Giants which he will cheat out for nothing and then duplicate indefinitely with his hero power, as soon as you start hitting his face.

There are two Rogue counters to this, either Mill Rogue where you empty his deck before hitting his face or a variant of Shuffle Rogue where you shuffle multiple copies of Flik Skyshiv into your deck, so that you can instantly destroy all his giants as soon as one has hit the board. This is the Flik variant.

Mulligan for Flik Skyshiv and Togwaggle's Scheme. Shadowstep is also useful. His early minions you can finish off with your hero power weapon.

Use Betrayal, Walk the Plank, Envenom Weapon or a Flik Skyshiv + Shadowstep combo when he starts putting out his big minions. Other than the Molten Giants, he only has one or two copies of his minions in his deck. Once Togwaggle's Scheme is upgraded to shuffle multiple copies of Flik into you deck, do it. Once Flik's back in your hand you're ready to hit face and destroy Avalanchan's Molten Giants when he plays one (or several).

For some reason the AI prefers to copy Khartut Defender despite silencing it immediately. Use Shadow of Death on a Khartut Defender in order to stay healthy and see Avalanchan produce mediocre copies. Even better if combined with Kel'Thuzad...

Don't play Academic Espionage before you have Togwaggle's Scheme and Flik in your hand. If you do, it could take some time before you get the needed combo.

By the way, using Alexstrasza and finishing him quickly is one way to walk around the milling/shuffling exercise.