When I play as Cthulhu during certain games, my general strategy is to primarily work off of his Cosmic primal power. Which is the capability for a free convert when a Seal is unlocked. This allows me to convert a stack of cultists in my or opponents pool. This leaves me to fish, look and hope that I get an assortment of certain cards. I start by laying as many 2 stacks of matching cultists or cultist/grimoire combos. Then by utilizing an Elder Sign, Steal Elder Sign or even Whispers of the Void will kick off one seal. Allowing me a free convert, which will potentially give me at least another seal by collapsing two Cthulhu Cultists with the other two cultists that were just converted. Now there is a chance that other players will have at least one Cthulhu Cultist and a stack of their own Cultists. using my second convert (as a free play due to unlocking the second seal) I can convert their cultists to Cthulhu and play a masters call to capitalize on another Ritual circle to unlock a third Seal for a third free convert. This sets me up for going out the next round.
Usually this is more likely of a play at about four to five rounds in and if it can be pulled off due to certain peoples play styles and cards obtained during draw phase.
Focus points for strategy
1) Only create 2 stacks of all cultists ( Leaving Cthulhu Cultists last to avoid Convert Cultists / Masters Call Combos played on you)
2) Curate your hand to have at least one Masters Call, One Elder Sign/Steal Elder Sign or Whispers of the Void
Cons and things to look out for
1) Barrier Spells will stop your plan if you dont pay attention to your opponents strategy causing you to be wide open to be picked over from other players.
2) Exclusive Eldritch Power Cards that shuffle, discard or swap players hands.
3) Cannibalistic Endeavors