Question: I am trying to make an original character who is blind
and hunts with bow and arrow from a flying mount. 
(Obviously, no existing animal can fly while bearing the weight of a human,
so let’s assume that the mount is a mythical/fantastical species;
for instance, a dragon or a gryphon.)

What physical qualities (internal/external)
would enable and enhance the archer’s feasibility and hunting prowess?

Answer: 
Very acute hearing, like that of a barn owl. Barn owls can hunt in complete darkness and without an active sonar like bats.

All owls have one ear pointing up and another pointing down so they can pinpoint sound sources more accurately. Their disc-like face also acts like a parabolic antenna for sound. The ears are hidden beneath the facial feathers, one aimed forward-up and the other forward-down.

Your hunter may wear an owl-mask to help them locate prey, or it may be descended from owls somehow.

Failing that, an active sonar like that of bats and dolphins would be a way to go, too.
How about ability to see/detect minute alterations of Earth's magnetic field or electricity? That might allow him to detect live beigns from a distance. I assume a medieval background due to the presence of mythical creatures so no radiowaves everywhere to drive him crazy, though his perception of a thunderstorm would be interesting.

Can't imagine the kind of organ which would allow, I can only think it would have to be duplicated to allow triangulation for distances. Maybe replacing the eyes?