I went through all the episodes trying to find ones that would have interesting MU equivalents, but there aren't many. For instance, any episode that begins with them on a humanitarian mission or answering a distress call would never happen, nor would most episodes starting with pure research missions; any episode about them resolving a diplomatic crisis would be over in minutes because they'd just blow everything up, so there wouldn't be much of a story; and episodes about battling cosmic threats or things that attack the ship would turn out largely the same, so there wouldn't be much point in telling it.
I figure the MU crew were just doing dastardly deeds that took roughly the same amount of time. Pirate raids instead of humanitarian missions, CAUSING distress calls instead of answering them, that sort of thing.
That doesn't really work, since many of the characters were not actually evil in the Mirror Universe, or at least were less evil than others (Forrest, Spock, most of the humans in DS9 MU) and some "bad"/"evil" people were "good" in the MU (Brunt).
I was just talking about the original TOS episode & not really factoring in what DS9 did with the MU later on. Sorry, should've been clearer.