I didn't experience this problem personally when playing through it, but I can still give you my recommendation as to what to do to possibly fix it. My recommendation would be to delete "The Walking Dead: 400 Days" off your hard drive or whatever you may have it on and then re-download it. Before you re-download it though, you may want to also delete your profile off your hard drive or whatever you may have it on and then recover it.
Once you do that you can attempt to replay the stories you played and see if the achievements unlock. If the achievements you should be unlocking don't unlock then, then I recommend you should address this on Telltale Games' forum, and more specifically in the sub-forum, "The Walking Dead - Hints and Help". Said sub-forum is located in the forum, "The Walking Dead", just in case you have issues finding it.