This achievement is hard to achieve, however this tutorial will show you a loophole to achieve it easier but still legitimately.

1) Start the mission "Vendetta".
2) Play through the level till you are required to kill the sniper in the opposite building.
3) Kill the sniper.
4) Look around the room on top of the tables and pick up the pistol nearby.
5) Play through the mission until you are required to kill General Amsel.
6) Snipe his henchmen and wait for the truck to come and collect him.
7) Snipe the truck a few times and shoot two magazines into it with the pistol.
8) Wait until General Amsel is next to the truck or about to get into it.
9) Fire the last magazine into the truck.
10) The truck should blow up killing General Amsel.
11) Since you blew up the truck with a pistol, you killed General Amsel with the pistol and the achievement will pop up.

Here is a video tutorial showing the end of my tutorial: