Check what challenges I have completed during a mission

After completing more than 2 but less than 5 challenges, a second unlock will be revealed - while the first is a character perk, the second is a weapon. The weapon will be unlocked after 5 challenges have been completed. If you complete 5 challenges on your first run you will get both unlocks, otherwise you can replay the mission later to get the unlocks you've missed.

I wondered this myself, I started the campaign over and over by going onto the "new game" option on the main menu. At the time I didn't really care about weapons and challenges, because I assumed that it would be a simple task after Veteran was completed; now that I have done Veteran and have gone through the challenges, I've realised it to be no simple task. In short, go onto "replay mission" and press RB to reset the mission progression. I think by doing this all challenges and guns may still be availabe.

I'd recommend starting a new game on a new profile, doing a challenge or two on recruit and complete the first mission, afterwards go to "replay mission" and see if they stay.

I wouldn't want to lose you tens of hours of play time. I hope this was helpful.