Stormrise

Due to the lack of online play, boosting is by far the easiest way to accomplish this. This is also achievable during the story mode or through skirmish, but it is fastest to boost it with a friend. Simply have one side make an army and the other side send broodlings into it 1 by 1 until this pops. If both players boosting this need the achievement, make sure you both pick the alien faction.

You need to spawn a Matriarch unit and use it's special ability to create broodlings.
-Thanks OfficerBarbrady

planting42's guide surely works, but I don't agree with him that it's easier to boost for this achievement.

In mission 4, you start in a cave with your 2 commanders. In front of you are 1 Matriarch and 1-2 groups of broodlings. This is where I got my achievement.

First, I completed the campaign on easy, where I got most of my kills. After the 12 missions, and went back to mission 4 and started it only 2 times (!) and got the achievement. What I did is:
1)Start mission 4 with mission select
2)Kill the broodlings and Matriarch
3)Advanced with Geary to the next Matriarch so he gets killed
4)Press Restart

As I said: if you already have a boosting partner for other achievements, you might as well boost it. But if you're done with the solo campaign and want to get this achievement fast, simply load the beginning of mission 4 a couple times and you'll eventually get it.

EDIT= I just started a new campaign on hard, and I realized that mission 1 (not the tutorial) has a few broodlings right at the start. Hence, you can use mission 1 or 4 to get this achievement.