The shotguns in Umbrella Corps work very similarly to shotguns from the Resident Evil series.
Shotguns have a large spread and are incredibly powerful at close range, which means they can often take out an enemy in one hit even if your aim is off or you aren't aiming for a headshot.
Use shotguns in closed areas, as long as you can aim even slightly they usually work out better than Brainers. The flip side is they lose most of their damage as the gap widens between you and the enemy. They can be useful for taking out jammers due to the large number of pellets fired. If you're using a shotgun it's a good idea to equip a handgun to cover mid- to long distances.
Depending on the match rules shotguns can make a big difference, such as in DNA and SP DNA Hunter modes, and they are also great for taking out opponents who attempt a Brainer lock-on. One of the more effective tactics is to shoot while moving backwards.