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: 
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.)
Hidden power
=============

Your character has a hidden power that permanently allows them to see into the future. Hence their current eyesight has been traded for one out of sequence with time. They know where the arrow will be once they let go for they see it already having arrived. 

To make sure this is not OP this could be limited to an enhancement / curse given by the bow they wield and only bestows the future location of arrows potentially fired from it.