I've only played against him once... and lost... so I don't think I'm the one to be handing out strategy here. For me, I was just at a loss as to how many provisions I needed to gather before heading out since there was ZERO guidance on this point.
And for what it's worth, I've played against the Dark Pharoah once (and lost) and Cthulhu maybe a dozen times (and I THINK I won once but my memory may be off there). I've beaten all of the Great Old Ones that came with the game though!
Ithaqua is the only Great Old One I haven't defeated yet! It's really frustrating when you're doing so well, at least one might think, and then only to randomly lose all your supplies, which requires an immediate reset.