As I am a achievement hunter by myself, I can totally understand that this is an annoyance. I guess you guys have already tried to restart the mission and check if the Dogtag is still there? It can help sometimes to properly reset the console:
1. Keep your finger pressed on the X1 icon on the console until it is shutting down
2. Unplug it from the power source for roughly two minutes
3. Connect it to the power adapter again and boot it up
If that won't help, I recommend to try at least once to delete and re-install the game on your Xbox.
Please keep us updated.
Basti