Backstory: I made a lot of C'Thun decks including Reno shaman, Reno galakrond rogue, Galakrond rogue, warrior, paladin, druid, warlock and was testing them all to find the best C'Thun deck. None of them are very competitive, however this C'Thun shaman deck, after a lot of changes, proved to be the most viable option.
This deck is not recommended for climbing ladder in diamond, however it might do ok in lower ranks where there are less competitive decks. Mostly, this deck is for fun and winning often enough against even tier 1 decks makes it a better choice to play.
The strength of this deck is the speed with which it combos. You can execute the combo on turn 10 and have C'Thun drawn somewhat consistently. It has a very good matchup against slower combo decks like lifedrinker Shudderwock shaman and exodia paladin in my experience due to this. It even has a good matchup against Reno priest, they play few minions and you can finish them with C'Thun more often than they draw all their combo pieces. Finally, it does well against slow control decks and basically autowins against odd warrior and dead man's hand warrior and can win against slow reno mages and warlocks as well. However, the main weakness of this deck is aggro. Your minions are often understatted and the only way to win is to get lucky with Evolve or Bandersmosh.
Another strength of this deck is its greater resilience to dirty rat than decks like Togwaggle druid, exodia paladin, or lifedrinker Shudderwock shaman
This is because if you lose Shudderwock, you can use your hero power after the quest is complete to buff C'Thun to otk levels, and if you lose C'Thun you can shuffle him back into your deck. Furthermore, there are a lot of minions in this deck as opposed to Togwaggle or Malygos druid so it is harder for Dirty Rat to hit your combo pieces.
Combos and win conditions
Electra Stormsurge and any card draw: draws a lot of cards, but she can also be used with evolve if you really need tempo
Play Grumble, Worldshaker and Doppelgangster then Shudderwock for infinite 1 mana shudderwocks that buff your C'Thun. He can be buffed to incredible levels but his damage is capped at 100. To increase the chance of Shudderwock going infinite, play Emperor Thaurissan and use the quest hero power the turn you play Shudderwock for 8 mana
Therefore, the deck is flexible in that you can play C'Thun first and then infinite damage dealing Shudderwocks or Shudderwocks to buff C'Thun first and then C'Thun to deal up to 100 damage later. For more tempo, it is often better to play one of your win conditions when it is ready and then play the second win to win if the first one is not enough (sometimes just a buffed C'Thun is enough without Shudderwock).
For the mulligan, always keep the Quest and try to get 2 cost minions.
Quest Mage: unfavored but possible to win if they draw poorly, try to draw as fast as possible to get to your combo first and use minion pressure with evolve to rush them down
Jade Druid: favored, you can draw very quickly and buff C'Thun to a high enough level where their armor is irrelevant
Cube Warlock: very unfavored, they have a lot of minion pressure and this deck can not handle it
Reno Priest: slightly favored but it depends on the version of reno priest, slower versions like anti aggro and dragon are more favored
Reno Quest Mage: slightly favored, after the nerf they are slower than you
Even Shaman: very unfavored, they have a lot of great minions but a good evolve can hold them off until turn 10
Secret Mage: very unfavored, there is no healing
Odd Warrior: very favored, they have no dirty rat and you can combo them down
Dead Man's Hand Warrior: favored, they usually only run one dirty rat and it has a low chance of stopping all of your combo win conditions
This is mostly tier 1 and 2 decks, the rest did not come up often enough but in general it is favored against slow decks and combo decks that combo slower than it and unfavored against aggressive decks
So, obviously it is not a good deck for climbing unless you happen to have a meta with a lot of priests, druids, and warriors, however it is fun to play C'Thun, and if you miss playing him it is worth it to try this deck, as out of all C'Thun decks, this is probably the best. Most C'Thun decks are way too slow now, if they go the anti aggro route they don't draw C'Thun consistently and do not have it buffed to the same level as the Shaman quest allows it be, so that when they play it the first time it is usually not even a otk. If they do focus on buffing in a class other than shaman which has Shudderwock for infinite buffs, they have to include too many buff cards and do not have enough card draw. Even in shaman, reno shaman can win more against aggressive decks but often gets outvalued against slow decks and almost always loses to combo. Therefore, after all my experimenting I have found that a combo version of the deck with quick draws and Shudderwock is the best for C'Thun.
This is my first time writing a guide, please let me know of any suggestions as to what to add to the guide and how this deck can be improved or any questions about it.