I see. It seems your problem is that the DLC achievements aren't registering properly. I vaguely recall having heard others with the same problem back in the day... But I don't remember how they fixed it. Or if they did.
Looking at the technical support forum, I see a thread here with someone having the same problem. If you look at the 3rd post, someone from QA says: "As for DLC achievements not unlocking on N7HQ, this is a currently known issue"
Seeing as that was 2½ years ago, it looks like you might not be able to have the issue fixed... But you could always try bumping that thread or create your own and hope that someone comes along with better advice 
Edit: there's another thread detailing the same problem and a possible way to fix it:
"I had the same issue with achievements and was trying to fix it ... i have the feeling that these steps solved it
- Start the game (without playing multiplayer otherwise quit and restart the game)
- Check your achievements in game, in Extras menu. (you achievements should be missing here)
- Load your last save game (or resume)
- Return to Main Menu
- Check your achievements in Extras menu (they should have appeard)
- Start multiplayer
- Check your N7HQ - in the better case it should be updated..."
Worth a try?