I used Chapter 2, Level 18 on 1 Star (easy) as this only has 1 trooper ensuring I gave my machine gunner the best chance to score the killing shot. Make sure to use the machine gunner specialist as often as you can in the Campaign missions. It only took me 2 plays-through of this mission after I'd completed the campaign to nab this achievement.
The Machine Gunner is
$30,000 $40,000 $50,000 (thanks to janiwesterling and mosin360 for the new prices) and doesn't unlock until after Level 16.