I’ve gone for this achievement several times and killed the Queen seven times in total. I didn’t unlock it until my last run. The only difference between my first six attempts and the seventh was that I kept shooting the Queen nonstop once I knew its health was low.
I’m fairly certain you need to be one of the last players to hit the Queen to get the achievement. If you jump to 17:12 in the video, you can see I was continuously firing at her, and the achievement popped the moment my shot connected, right before the Queen died.