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: 
Some sort of ESP-like ability, which would allow the protagonist to either pinpoint another being, or possibly permit them to see through the eyes of another creature. Note that if they've been blind from birth, the ability to see through the eyes of another probably won't help unless they've had a lot of experience hunting this way.
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?