It is possible to earn this achievement during two duels, those being Pat Garrett, the first duel, and Old Man Clanton, the third duel available during the Dueling Challenge. Clanton's is the easiest in my experience because the bird perched behind him on the rock doesn't move and is often a relatively easy target. One only needs to get enough focus and draw speed to be able to kill both the bird and the opponent without getting shot.