First Encounter TOS 2.04 Mirror, Mirror Terran Rebellion DS9 2.23 Crossover DS9 3.19 Through the Looking Glass DS9 4.20 Shattered Mirror Rise of the Empire ENT 4.18-4.19 In a Mirror, Darkly, Parts I&II Other Encounters DS9 6.08 Resurrection DS9 7.12 The Emperor’s New Cloak Additional Viewing TOS 3.09 The Tholian Web
This is really more like three arcs that all deal with the same setting but are a joy to watch anyway.
Mirror, Mirror is a great introduction to the barbarism of the setting and exactly how at odds the MU is to the prime universe. The Terran Rebellion as told on DS9 is an interesting arc that shows the repercussions of Kirk's actions and moves the timeline forward. In a Mirror, Darkly is a lot of fun and I greatly enjoy the writing and so many aspects of the approach and execution. The more I watch Enterprise the more I wonder why people disliked it so much.
The other episodes are entirely skippable. The two DS9 installments are kind of afterthoughts that reference or revisit the earlier episodes. Neither move along the story or characters. The Tholian Web is only peripherally related as it is heavily referenced in the ENT episodes but not directly related otherwise.