See Pistol Mastery for more info.
The shotgun handles critical hits almost exactly like the pistol. Whenever you're aim is zoomed in with , you will see two bars, at the top and bottom of the crosshair's respectively, begin to circle around the crosshair's. Once they've completely circled around, your shotgun will perform a critical hit with your next shot. You'll know you've done it right if the shot knocks down whoever it hits.
If you have invested into the shotgun tree, the Room Sweeper ability will make this achievement much easier. For the duration of the skill, every shot will be a critical hit, so you can get this achievement very quickly with it.
You will unlock the perk "Shotgun Rampage" after scoring fifty critical hits with the shotgun.