Howdy!
When I boot up the master archives, it says I can’t get achievements because of cheats. But I have beaten the entire campaign without cheats, and just now even tried restarting the campaign, but when going back to master archives it still says the same thing. I want to be able to use to the master archives for the 10th anniversary achievements,
how can I reset the cheat/no achievement flag for the master archives?
Go to bug report. 2020
I guess this is either just a Me problem, or so common no one wishes to help 
You said you tried restarting campaign, but have you finished another campaign playthrough? I do NOT know, but guess it might be possible that a whole new campaign playthrough could somehow reset the Master Archives, eliminating the faulty cheat block. Can NOT promise though, as I’ve never faced this myself.
I bet all HOTS 10th Anniversary achievements can be done at least on normal difficulty even via normal campaign playthrough (that is, despite not having as much unit tech & Kerrigan abilities as when playing via Master Archives). However, do note that if you’re doing Anniversary achievements by normal campaign playthrough you must go to Skygeirr missions BEFORE “space missions” (where you go for Jim Raynor), because you need to have Infestors (unlocked in the 1st Skygeirr mission) to do the Anniversary achievement in the 2nd space mission.
(EDIT: Of course, after completing the campaign you could do this achievement via Master Archives no matter which way you advanced during campaign since Infestors are then always in 2nd space mission - but of course this depends on actually being able to play Master Archives…)