Go to Rhodes town to look for Billy Midnight. Reach the train station. Speak with the station clerk. Ask him about Billy. (the yellow dialog option.)
Get into the train that has just stopped on the station. Keep moving through the carts until you reach the bar cart. There, you will find Billy Midnight. (the picture above.)
Billy starts to escape – follow him. Keep moving through the carts. After a while you will have to climb on a cart. This is where you will catch Billy. The man challenges you to a duel. Press the right trigger only about halfway and shoot once the bar is full. Kill Billy before he shoots first. You can hit any of his body parts.
Approach the gunslinger’s corpse. Take out the camera from your inventory – this item is in the same slot as binoculars. Take a picture of dead Billy Midnight.
Search Emmet’s corpse – you will find Midnight’s Revolver, a unique weapon.