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.
Hidden power
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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.