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.
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.