The sheriff is the boss at the end of the Train stage.
First, the sheriff will throw TNT at you. You must pick up one of these sticks and throw it back. If done successfully, the sheriff will take damage and then start shooting at you from a minigun.
At this point you must take cover behind a barrel by pressing
. Next, you will take aim in the shooting sequence. This is the part where you can't miss. There doesn't seem to be any time restriction during this part (aside from you barrels getting destroyed), so you can take your time before firing your shot (
You will notice quickly that the pattern of you crosshairs is repetitive and somewhat predictable. There will be one part of the pattern in which the crosshairs will slow down near the target. This is when you will want to take your shot.
It may take some practice before you get the timing down. If you mess up, I am pretty sure you can let yourself get killed and restart at the boss (as opposed to restarting from the menu, which takes you to the start of the stage). Can't confirm this.
Anyway, one frustrating part is that you will get the boss down to virtually 0 health and think the fight is over, but will still require an additional hit to finish.