Best guide for this achievement is get a better weapon! lol, nah, just ensure you not quit the game and grind it till you get the award, hopefully it dont crash aswell.
If your wanting to know how to fix your stats not updating, its best to delete profile on the xbox, then redownload the profile again, I had this issue where it was stuck on 854 kills, then after redownloading my profile, it updated to 879 kills.