Any kills made with any of the 3 weapons at your disposal will count toward the achievement, but it is recommended that you stick with the Gatling gun until the tank arrives in Wave 5. Enemy soldiers running down the rails to the right of your position will not count toward the achievement, so don’t waste time with them, focus on the area right in front of you and the sniper positions.
In Wave 2, snipers can be hit at distance with the Gatling gun if you wait until their light is shining right at you and aim for the center of the glow. Also, there is a relatively close catwalk on the left side on which snipers routinely appear and are easier to hit, so make sure you take these guys out every time they show up.
In Wave 3, be sure to kill all the shield soldiers before the Gatling gunner as he will explode taking down any remaining shield soldiers, robbing you of the kill count. Also, for additional kills, since snipers still spawn allow the shield group to advance a bit and take out as many of the re-spawning snipers as you can before destroying the shield group and gunner.
In Wave 5, while difficult to hit, the soldiers on the tank count as kills, but the tank itself will not.
If you’ve managed to kill virtually everything up until the tank arrives, the achievement should pop right around that time. If not, you will have to try again from the beginning.