There have been multiple threads in the bug report forum about Achievements not unlocking in Competitive. I think this has to do with how Role Queue Beta is setup similar to that of an arcade competitive mode (same reason why win rates are not showing in the career profile). This is a speculation on my part of course. No confirmation made in any forum thread from what I have seen.
This is a bug that Blizzard is aware of the issues of role lock without any role selection affecting the Practice Vs. AI modes. Unfortunately, they stated it will take an actual game client patch to fix.
EDIT/UPDATE, Just as I posted that response we got the Game Client update fixing this issue.