This isn't a walkthrough of any mission in particular, but just a couple of tips I noticed.
One, the sub-missions appear to unlock randomly, or at least, after beating story missions. If there's more to it, I'm not aware.
Two, play them on Easy. It appears that clearing them on any mode counts, and switching to easy for the challenge missions won't affect switching back to Normal or Hard for the story missions, if you're doing that also.