From The TimeSplitters Wiki

The Shotgun is a very powerful weapon, but only holds 2 shots at a time. This means that you can only fire twice before you have to reload. The Shotgun is extremely effective at close range, a close-up shot to the head can be an instant kill. Before you go into any engagement with an enemy, make sure you have your 2 shots loaded. The time you spend reloading is when you are most vulnerable since the reload time is so long. You should move in as close as you can before you fire, and move around in a random pattern while you reload. This makes you much harder to hit you, and you are able to do lots of damage to your enemy.

The Shotgun is nearly useless when fired from long range, so always get as close to your enemy as you can for maximum effectiveness.

The Shotgun has appeared in every TimeSplitters game so far.