This isn’t so much a guide as an explanation of what I encountered at launch. I completed all Avengers Iconic Missions after completing the campaign and didn’t get the achievement. I continued on with the ‘Reigning Supreme’ post-Campaign mission chain. Upon completing Step 6 (which was to complete three different elite villain sectors), the achievement unlocked.
Maybe they’ll fix this in a future update but I did notice Step 7 of the ‘Reigning Supreme’ mission quest includes “Complete the Iconic Avengers mission chain” so it appears the achievement popped when I got to the point where this mission quest had asked me to complete it (which I already had). So if you don’t get it when you complete all the missions, continue the ‘Reigning Supreme’ mission chain and it may still unlock at this point.