Card Choices

No 1 mana drops

Since it's hard to consistently have them in the initial hand without filling the deck of useless late game cards, I ended up removing all small drops to have better chances later in the game. Taking the first 10 damage is not a  big deal with the amount of healing available.

Recombobulator

Great to deal with Living Bomb and to get better value from Antique Healbot. I have only one but if you have two you can remove a Shiv and add it.

Shiv

I don't have Bloodmage Thalnos, and I needed the extra card draw. It's also useful to ping the Magma Rager he drops. 

Preparation

It's often a dead card when you want to spend a lot of mana every turn. But having  a 3 mana Vanish is needed sometimes, so I included one.

Grim Patron

If you manage to trigger him and then Vanish him back to your hand he will win you the game, if you manage to dodge Hellfire, of course. Feel free to replace him with anything else, it's probably not needed.

Anub'ar Ambusher

I think a 4-drop is essential in this fight. But I included this card just before I beat the boss so not sure it's the best one. Its deathrattle can be very nice in this deck and its stats allow you to kill all of Geddon's creatures except for Molten Giant.

Sylvanas Windrunner

Great for dealing with Molten Giant and/or steal Fire Elemental. You could replace it with Big Game Hunter. Actually I considered crafting a Big Game Hunter but in the end I didn't need it.

Strategy

It's not necessary to really mill him much, just outlast him and keep consuming your mana.

Use Gang Up on Antique Healbot to outlast him, but  you need to do that near fatigue or you'll draw the healbots when not needed.

Keep in mind he'll start dropping Molten Giant when low on health. Be sure you'll be able to deal with them. Save up Sylvanas Windrunner or Vanish if you can.