First, there are two Nyarlathoteps, two Wilbur Whateleys, two cost-6 Cthulhu's, and three Yog-Sothoths, which ones is she using? Not that it makes THAT big a difference.
Second, most Cthulhu discussion is on Cardgamedb.com. You may want to get an account there and they also have an excellent deck builder so you could post your deck in a more readable form that lets people see the cards. The easier it is, the more replies you will likely get.
Then, the deck. You probably don't care at this point but this deck is not legal as it has three different Restricted cards: Nyarlathotep (assuming you're using The Black Pharaoh version and not the one that came out a few days ago), Broken Space Broken Time, and Ravager from the Deep. Sine they are all 1x's though, it's not a big deal. Also, as you know decks only need to be 50 cards so it could be trimmed down quite a bit. Again, it sounds like you're just doing your own thing at home and you're both operating under the same rules so probably not a big deal.
I don't know what your deck looks like, but this one doesn't seem particularly strong. She has very few low cost characters, which means that she will have trouble defending early in the game. I would think that nearly any deck with a better cost curve should do well against it. Plus it has the disadvantage of being inconsistent with almost everything being a 1x.
Just to check, you must pay for a card with a single domain, you cannot combine them. That's the only thing I can think of that would make a deck of predominantly high-cost characters more viable.
A decent Mi-go deck should do well, although it's far from your only option. In addition to the Mi-go themselves you would want some acceleration in there such as Priestess of Bubastis, Feed Her Young, etc... and then supplement with some more cheap guys to help cover the early game. Black Dog would be a good option, and I'd also suggest Book of Iod to help your draw and improve consistency. If you want a second faction you could blend with Miskatonic or Silver Twilight and get access to some cheap Investigation and more shenanigans.
Or, you can shift gears and go with a different deck type. For instance, you might try Syndicate and look for cards that can exhaust her big guys. Lots of options.
What I would suggest is that you tell us more about what happens in the game that you are having trouble dealing with. Not just specific cards, because at 1-of-75 it's highly random whether a particular card shows up. But in general, what is the flow like and where do you run into trouble?
Also, can you tell us something about your resourcing? This is one of the biggest "invisible" reasons you can lose because it's easy to gloss over the cards you don't play - they tend to be forgotten. You should be keeping some inexpensive characters from your initial 8 cards and resourcing expensive stuff, duplicates, or cards you won't play for a little while.
Finally, what do you have to build from? It sounds like your card pool is pretty good but I don't want to suggest cards you don't own, that doesn't help
Shame there isn't a "Guyver Defence Mode" card that allows you to just destroy everything in its path.
Anyway, I'm writing just to say that I feel your pain, rather than to offer any advice. I'm in a similar position where my partner has started handing my arse to me in every game using her Shub/Mi-go deck. It has no bells or whistles, it just breeds. And breeds. And when you cut a bloody swathe through the breeders, they just come back into play at the same time. On the one hand, it's crushing, but on the other hand, it's quite fair because my Yog deck was the one to beat in our household for ages. Now the boot is on the other foot and I've just had to roll with the punches. To make matters worse for myself, I've just gone and bought her the new Shub deluxe expansion (I'm hoping she doesn't snaffle up particular cards that I have earmarked to work in a Cthulhu deck, but we'll see).
The only advice I can offer, off-the-cuff, is Hastur cancellation or hand destruction. Can't bring anything into play if her hand is empty.
That represents one of the keywords: Steadfast, which you will find explained on page 12 of the Rule Book. The symbol means that you must have that many resources among all of your domains in order to play the card.
It would've been smart of them to have included some note about it in that card anatomy section, given they specifically chose a card with Steadfast for that diagram.
