So today I finally got the C'Thun achievement using a Priest deck. I mentioned earlier this Druid deck that uses Aviana, Kun, Ysiel and Tree of Life, but as I don't have these cards, I had to try something else, so I went with a Miracle Priest deck. There are many videos on youtube of people killing their opponent with C'Thun, the Shattered, sometimes as early as turn 6. Here is a quick guide on how I managed it, it only took me 3 attempts (3 games) in total:
First of all I did it in wild, where you have some additional useful cards like Shadow Visions and Regenerate, but also because there is where I have tanked my MMR by playing meme decks for the achievements and thus I am more likely to avoid top tier decks.
Secondly, you need to face a slow deck that won't kill you by turn 5 and that is not a Warrior or Druid that can armor up out or range.
Deck building: The key cards are: Nazmani Bloodweaver and Gadgetzan Auctioneer (these are the only minions in your deck). Insight (to draw and discount your key minions), Gift of Luminance (to copy Nazmani), Palm Reading (the discounting effect is great), Raise Dead (get back your key minions after they died once). The rest is various 0- and 1-mana spells
Execution: On a preparatory turn, ideally with an Auctioneer already in hand, you will play a Nazmani followed by a bunch of cheap spells. If you can, do play a Gift of Luminance on it too. The goal is to discount the cost of Auctioneer as much as possible and you can get back 2 Nazmanis later from Raise Dead. Then on the Miracle turn you play as many Nazmanis as you can and the Auctioneer and begin drawing through your deck by casting cheap spells. Important: as the animations are too slow, avoid playing any spell that discovers a spell (Renew or Palm Reading) at this stage as you will then have to wait for the animations to finish before you can get to choose your discovery. If you are really fast, you can draw through your whole deck, play all C'Thun pieces, draw C'Thun and play him on the same turn. I only managed to play 3 C'Thun pieces but I had the remaining one in hand, discounted to 0, together with a corrupted Insight (to draw C'Thun for 8 mana) which was also discounted to 0. This was good enough
Important: You need to kill your opponent from full health. But when you cast Eye of C'Thun, you will almost certainly damage a bit the enemy hero. Which means that you need to heal them back up to 30 before the kill. In standard you only have Renew and your hero power. In wild there is also Regenerate which helps a lot.
P.S.: The new achievements based on the Darkmoon Races cards are all quite easy and straightforward, I don't think a guide for them is useful