Once Trogdor is out of the machine and the ghosts are out of the House Of Strong, go to a redcoat ghost found somewhere in the field. Take out your light musket. If you miss it, The Cheat will come out of nowhere and laugh, similar to how the dog on Duck Hunt appeared.
Once Trogdor gets out of the machine, go to the House Of Strong. Get the ghosts out of the House Of Strong by helping all four colonel ghosts (the blue ones). After that, go out to the field. Somewhere in between the cool car and the photo booth is a redcoat ghost. Shoot it with the light musket. When you check the game stats, under the "Video Game" section it should read "Redcoat Ghost Patrol" and that you have 100 points for it. To get more points, go to the same place. Shoot the redcoat ghost until you get the desired amount of points.