The Lamplighters League

Thought this was unobtainable at first but after seeing a few unlocks popping up decided to test some things out and it seems that you have to defeat her in a single turn, possibly on Survival difficulty and possibly without killing any of the other enemies in the area. This can be done on any difficulty and you can clear out some of the enemies before starting the turn-based combat.

In order to defeat her in one turn you need to hit every shot, or get 2-3 crits per miss, you also need to recruit the pilot first, you can easily recruit the pilot with Lateef by just walking around the stationary guard to the building, wait for his red circle to go down a bit then go back in to get the pilot, try to lure the patrolling guards when doing this to make it easier to get back to your group. Once regrouped head to the dynamite box near the dock and wait for Lady Nicastro to be within it's radius, try to lure her away from cover before starting combat then using Eddie, shoot the box and Lady Nicastro. Now it's just a case of unloading all your attacks on her.

I recommend saving at the start of this area before rescuing the pilot, and save again after rescuing the pilot, make sure to reload your save if you get caught by the patrols or miss attacks on Lady Nicastro.

Achievement will unlock as soon as she retreats. I did this on 2 accounts to test it and it works on Xbox and PC, both were on Survival difficulty and Lady Nicastro was the first enemy to die in that area both times too.

Video for the full mission below but you can skip to 1:59 for the final section or 3:25 for the fight itself.

The Lamplighters League - A Hasty Escape - Tables Turned Achievement