This is easily done as an add-on to a side mission instead of trying to hunt down three ships in a story mission.
I did it on chapter 3. I started a side mission, completed the objectives, and then when the "mission complete" message flashed up and the game instructed me to return to Shard, I headed over to Stargazer instead (which is automatically an enemy faction in this chapter).
Start shooting at the turrets on top of Stargazer and a ship, an airship, and two dragons will spawn. Take down the ship (and the rest of the enemies if they are too much bother - it wasn't too much of a problem on easy*), then head out of view of Stargazer, giving the enemies a chance to respawn, then head back. Rinse and repeat until you've shot down three ships, then head back to Shard to officially complete your side mission. The achievement should pop immediately!
(You can also use this method to earn the Steel Surgeon achievement, which I did at the same time).
*Although it was cloudy weather when I achieved it, YMMV).