Multiplier is shown as a bar above your health bar. When this is light green instead of dark green, you have multiplier in effect.
Now, for this achievement you need to kill 10 people with your Special Ops Kit before the light green dissappear and turns dark green.
The best mission to do this on is Burning Bridges. Here you start out with Special Ops Kit. As you work your way accross the bridge you will encounter plenty of enemies you can shoot to increase your multiplier.
If you're having trouble getting enough kills fast enough, or before you die, note that after each time you arm one of the three bombs, a wave of enemies will approach. Taking these out greatly increases your chances of getting 10 kills fast enough.