When do Challenge notifications trigger?
Solution 1:
in theory, Challenge notifications will trigger the moment a criteria is met (eg. getting halfway through any Challenge, completing any Challenge, or whatever other criteria there may be). however, as with most other HUD elements--such as waypoint or mission changes, Duel or Trade requests, and so on--a sniper's scope overrides that HUD for its own. this will basically place the HUD elements "on hold" until the next available moment in gametime when the HUD can be updated, which would be (in theory) the few moments after your scope is put down.