Why I have not completed the achievement on xbox when I completed it in game?

Achievements unlocking in game is up to the developer specifically. There is nothing that xbox, xbox support, or this forums can do to correct the issue. I would continue to speak with Activision in regards to the achievement not unlocking.

Ah, okay - thank you for providing those examples. I can definitely confirm I see that on your profile. Unfortunately, we were hoping for the opposite - that they would be showing unlocked on the profile from our side. That would certainly make it easy,
but unfortunately in this case, replaying for those achievements is the only option. Very sorry we don't have a better answer!

If that happens, just download your profile again... sign out and then press the big "X" button and go down to "Download Profile." Be sure you disconnect from Xbox live and reconnect before you do it though, cause it'll download your profile as it was the
last time you reconnected to Xbox Live! Hopefully that helps

Well, I can give a few examples, in GOW3 the achievements "Reach Level 15" and "Reach Level 25" have not unlocked but I've reached Level 79. On Skyrim several quests I completed during my profile's little spaz moment didn't unlock, like "Hail, Sithis." Those
are just a couple examples, I'm sorry to hear you can't award achievements though... I suppose I will have to restart the games just to get those achievements if I want to earn them. Thank you for replying though!

Hey DRGY! Do you think you could give us specific examples of these achievements that show earned but have not unlocked or awarded GS? Do they show on xbox.com in your activity? The only possibility here - since we don't have the ability to grant achievements
- is to delete the game saves and try to earn those achievements again. Let us know about those examples though so we can explore further!