The above solution does work, however the best way I found to get this was during the Duel Mode.
I believe it's the third duel and it will be against Old Man Clanton. Follow his pattern, it's far right and then back to the middle.
Beside his right shoulder will be a vulture.
If you have great focus and speed you will have enough time to shoot the bird and Clanton without any issues.
Once you get his pattern down and both the focus and speed at about 90 or so, after a couple of tries you should be able to nab this puppy.