Would you feel better if I said he would finish him off with his swords?
The point is Muu can completely erase his presence to the point that he’s a non-person. Without a chakra form and presence, he can practically solo the majority of the Naruto universe (and he probably did).Itachi does not possess any sensor sand/rain, any special modes, or a barrier like Jiraiya so he can’t intercept Muu’s attack. This is based on the manga the pages are there, it’s not based on whether or not you or I think the technique is overrated. Until Kishi actually changes his mind or decide to reveal new info, it will stay canon and anything other than that can be summed up as baseless assumptions. Same can be said about his past battles since we are not privy to them (even though the 2nd Mizukage was, obviously, a bad match-up with his clam and jokey boy which can sense heat), or Muu’s progress for that matter, so it’s futile to bring that up when we are both full aware that only Kishi can answer that.
Itachi will simply lose his head with a single slash, from behind, probably a bloody scene, since Muu is not dumb enough to engage in a full blown battle when he can take advantage of his incredible invisibility mode while also avoid using a chakra-taxing technique that will reveal his position i.e. Jinton.
However, I will correct you since you either forgot or chose to ignore that Muu can take flight, at any moment, thus rendering amaterasu useless. Muu is also an incredible sensor, arguably the best (Naruto and Karin are also up there), he can sense Amaterasu coming and simply avoid it… just like he sensed the fastest man alive, Naruto, waited until the last possible moment and dodged a rasen shuriken with his back turned. How on earth do you expect amaterasu to play any role whatsoever in this battle?
Tsukuyomi can be avoided with a little thing called distance, or by Muu simply flying, by the way, while doing that Muu could blast Itachi with a giant Jintons. We already saw the immortal, invincible Madara fear/respect jinton after all his clones were completely erased, even with preta but I digress. The yata mirror will protect Itachi for awhile, but eventually Itachi will either die from exhaustion, chakra depletion, etc., or Muu will find his opening before that- behind the mirror. It’s a horrible, horrible match-up for Itachi, I don’t see intelligence changing anything here especially as Muu created a kekkei tota and is an intelligent shinobi himself.
As I said in the beginning, it won’t reach that far death by assassination will be the most likely outcome.