Check in on the Challenges menu frequently so that you are always focused on working on a challenge. You are free to work on multiple challenges at once, and it is recommended that you combine challenges in attempts to make progress on at least two at once. For instance, a challenge to complete 10 headshots on enemy Operators can also be completed while completing 10 headshots with Assault Rifles. This will kill two birds with one stone and earn you two different rewards with one action.