Hawks are often found flying around open areas. They usually make a loud screech when they are in the air. While difficult to hit, their feathers are worth 6 dollars each, making these animals an excellent way of getting money since 1-4 feathers are received for each kill.
There are fellow hunters with a bird shooting challenge spread across the Hennigan's Stead area. Shoot the hawks without starting the challenge, for there is always a sufficient amount of hawks in the air for the challenge to be done. If they disappear, start the challenge and some more should appear.
Like all birds/animals/people, a dead hawk becomes an x on the minimap when Marston kills them (if he is close enough). Birds are particularly hard to find once they are on the ground amongst the foliage. After shooting them down, run in their direction and look for an x on the minimap.