You must kill 40 individual enemies via shotgun blast or shotgun execution.
Kills don't stack upon death or reload. For example, let's say you have 0 total shotgun kills. If you kill 5 people then reload the checkpoint, you will start back at 0 kills. Even if you kill the same exact 5 enemies, your total will still be 5. Likewise, if you were to kill 5 people then die, your kill count would be set to 0 at re spawn.
Basically, if you're killing the same people over and over you will not get this achievement or any other relying on a number of kills. You must kill 40 individual enemies to unlock this. And if you're playing on hard, its a pain in the @$$. Good luck!