Woohoo!!! It took a while...but I finally got all of the Mirror Incursion Research DOFF (duty officer) missions completed with a critical rating! As a result, I got the nice little title of "Mirror Infiltrator" in Star Trek Online (and around 50,000 dilithium, which I don't have much use for at the moment).  This DOFF accolade had 10 missions to complete, and when I originally tried to play through these with just random DOFFs (not paying attention to specialization skills), I only managed to get a crit-rating on one.  Paying a bit more attention to DOFF skills and buying some ultra-rare doffs on the exchange got me to 9/10 done. The mission that gave me a lot of issues was "The Emperor."  For most missions, having a 29% critical rating would clear the mission with a critical rating after 3-4 tries, but this one was at least 10...  I think this was the last set of lockbox-based research missions that had 10 missions to play through.  Most of the subsequent lockbox-based research doff missions seem to only have five missions (and thank God for that...)

Once critical has been achieved, this is what you get the following little lore: "Though personal information about the Terran Emperor is deliberately concealed, your operatives learn that he is ruthless and capable of incredible feats. He has tendency to show up uncannily and destroy conspirators, and is believed to have served in Starfleet before he manifested his unusual powers. Thus far, he has been completely undefeatable."

I guess through the current set of missions (the storyline that's unfolding now in STO) we know that the Emperor is Mirror Wesley Crusher...

Now that I am done with these, I guess I can increase my Energy Credit wealth by doing research mission arbitrage ;-) Not sure what I'll spend the EC on, but it's more useful than dilithium for my game play.

As a side note...not sure of you can get a crit-rating by playing as lower decks characters 😂