Battlefield 1

For any newcomers to this game the "Challenges" actually equate to the actions required to unlock the campaign's Codex Entries, which also encompasses collecting all Field Manuals in a level.

To view a level's challenges/codex entries pause the campaign and you will see them to the right of the screen. You can click on each one to view the criteria required to meet them. Once you meet this criteria a codex popup will appear onscreen.

The use of the term "Challenges" can be somewhat misleading as this could be interpreted as something in addition to unlocking all codex entries and collecting all field manuals when you look at the achievement list (which it is not).

For a more in depth guide on each specific challenge/codex entry there are some good solutions already for each of the campaign's war stories and the Master of Adaptation achievement.