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.
This is somewhat generic
(i.e., it goes to support the feasibility of a blind rider
controlling a flying beast, and not so much the archery aspect),
but, since telepathy has already been mentioned:
a psychic link between the rider and the steed would be very useful. 
Even if it doesn’t go so far as to allow
the rider to see through the mount’s eyes (as [suggested by James](https://worldbuilding.stackexchange.com/questions/45212/#comment127266_45257)),
it would be very handy if the mount could alert the rider
to upcoming maneuvers, or if the rider could direct the mount,
all without making a sound. 
Compare to the [neural interface](http://www.avatarmovie.com/index.html) between creatures
(including the bond between rider and steed) in James Cameron’s [*Avatar*](https://en.wikipedia.org/wiki/Avatar_(2009_film)).

Also, you might want to look at the [Nazgûl](https://en.wikipedia.org/wiki/Nazg%C3%BBl)
(from *The Lord of the Rings*) for some general inspiration. 
While they are not totally blind,
they [do not see the world of light as we do](https://scifi.stackexchange.com/q/14876/30482#14880 "Lord of the Rings – Are the Nazgûl Blind? – Science Fiction & Fantasy Stack Exchange"). 
(They may use a sense of smell when on the ground;
it’s not clear whether that would be useful when they are airborne.)