It's actually a pretty common problem with DLC on xbox360ach. The solution is always the same, and has worked for me each time:
(1) Go to "My Checklists"
(2) Delete the game you're having trouble with (ACR) by clicking on the Red X to the right of it
(3) Re-add the game back to your games list
(4) Re-enter any achievements you've got.
You should now be able to log the broken achievements normally.