Challenges all war stories do not count !

This is what I did on PS4.

My issue on PS4 was for;

War Story: Nordlys
Act: Still and Silent

Challenge: Destroy all searchlights

The challenge "Destroy all searchlights" did not show as complete, despite completing it 5 times on different difficulties. But when I was in the actual Act, it showed as complete.

I'd finish the Act, start the next Act, but when I exited and went back to check the status of Destroy all searchlights, it showed as not complete. 

Also, if you try this, you will have to replay the BFV introduction missions before you can replay the war story Act that bugged out for you.

This is what I did on my PS4, but I don't know if it is the same in all regions etc or if it will work for you.

Please make sure you have backup copies of the game file before trying this.

BFV on my PS4 has one Auto save file, which is found in Settings, Application Saved Data Management, Saved Data in System Storage, Battlefield V.

Firstly, I copied the Battlefield V Profile Save Data file to USB Storage Device and also uploaded a copy to Online Storage.

Then I went back into the PS4 Settings, Application Saved Data Management, Delete, Battlefield V and deleted the BFV file.

After deleting the file, I restarted BFV, replayed the introductions, then went into Play, War Stories, Nordlys, Acts, Still and Silent (yours might be different depending on which objective bugged out for you), and replayed the mission only focusing on completing the missing objective Destroy all searchlights (yours might be different).

When I completed the objective, an in-game message popped up indicating it completed.

Then I went to BFV options and quit back to the game menu.

When I checked the War Story, the Destroy all searchlights objective showed as complete, but I was missing the previously completed objective info within the individual War Story Acts.

Next, I exited BFV completely, went back into the PS4 Settings, Application Saved Data Management, Saved Data on USB Storage Device, Copy to System Storage, Battlefield V, selected Battlefield V Profile Saved Data and Copy.

This returned the previously saved data back to the PS4 and all of the objectives I'd already completed as well as the previously bugged one was now showing correctly as completed.

Again, if you try this make sure you make USB backups before you attempt this work around.

I rarely check back on my posts, so please don't be upset if I don't reply to any questions.

Good luck, I hope yours is also fixed and most importantly, have fun out there.