In the Wild West booth, you will come to the Western Showdown mini game. This requires you to do a few things to make this happen. The clock tower is located to the right of the level, you can't miss it. There are a total of four targets attached to this building, which will cycle one at a time. Each time you complete a four target cycle the clock will move ahead five minutes. The clock will read 20 minutes till Noon. You'll have to do this four times. Stop the clock 5 minutes till noon, until the buffalo spawn.
The buffalo appear in the center of the screen, first as a single buffalo, and then as a group of two buffalo. Focus on hitting the first two buffalo, and spare the third one. Complete the four target cycle again, to make the clock hand move ahead to 12 o'clock. Then shoot the third buffalo.