Some challenges are tied to specific enemy types or allies, but they are all still possible after the story and getting 100% completion. Along the way you will complete many challenges without trying and you will unlock all weapons that are needed for challenges. You can still do all Challenges after that. The best approach is to finish all main missions first and get 100% completion in all districts.
You can check your progress by opening the phone, click the “Missions” app, press R1/RB to switch to “Challenges”, click a Challenge to see the progress. For the Perks List refer to Saints Row All Perks.
