Greetings Wnderfullock,
I am game master Yrodiate, and I have been in charge of reviewing your case regarding your inability to complete T4 delves since The War Within achievement has not popped out despite completing the campaign. I can understand how frustrating this situation has been since it damages your game experience when you just want to have fun. So, I will check it out for you to see what it can be done.
Now, I have done some research on this issue, and found that this could be an in game issue most likely related to a bug.
In case you think this issue is a bug, we strongly recommend you to submit a report via the support platform in game or in our forums so our dev team can check on it. Please note that even when they would probably not answer the reports, they will certainly look at them to track it up.