You will find many explosive objects scattered around the game. They are dark red and have a fire hazard symbol on them. They are scattered all over starting as early as the first chapter. Simply shoot ten of them and make sure that each time the explosion kills at least one person. If you kill more than one person with a single explosion, it still only count as 1 on the counter.
If you find a spot where there are enemies near explosives close to a checkpoint, you can just keep reloading the checkpoint until you unlock the achievement. I good spot to get this achievement is during Chapter 10, Part 2, where you use the grenade launcher from the side of the truck.