The exact opposite of Ladies' Man, you need to make sure that you do not romance any of the ladies in the game, or even make sure they like you. Safest bet, like Judge, Jury, and Executioner, is to make sure that they all simply just don't like you, or at the very least stay neutral with you. For the sake of this achievement however, you must view each of the scenes where you would get the romance achievement if the ladies don't like you. That means you also have to make sure you don't piss SIE off too much, as she must be your handler for the final mission. For how to handle each lady for this achievement, read on.
Mina Tang: Make sure she doesn't like you. That means being Suave with her in the beginning, and just being a jerk in general by responding to her with Aggressive answers and killing or beating the various civilians you encounter. Also, in missions that contain CIA, marines, local law enforcement, or civilians, make sure you kill them. Each kill will make you lose one like point with Mina, so that's huge.
If Mina talks to you via the TV instead of at the safehouse before the final mission, then you're good.
Scarlet Lake: Either Neutral or Dislike is good here. Do not send her anything incriminating towards Hallbech, and just use Suave and Aggressive responses with her.
You'll know you're good if instead of meeting Scarlet in her hotel room, you meet her in a restaurant. She also will not appear in the interrogation room during the final mission if done correctly.
Madison: Dislike is best thing to do, so aggressive answers are key here. Just do whatever you can to piss her off, and show that you don't care. Keep insinuating that she's in league with Marburg, and that you're willing to do whatever it takes to make sure she doesn't talk to anyone else.
If she attacks you after finishing the two missions following "Investigate Marburg's Villa", then you're fine.
SIE: SIE needs to be neutral, or even like you just a little, not up to Trusting. Contrary to the other women, go with Professional answers. She doesn't like by-the-book agents, so go with that. Also, do not choose her as your handler during "Intercept Surkov at US Embassy". Make sure that you do choose her as your handler during the final mission. Try not to get her above +4 like, if possible.
When SIE comes to you while you're in the Medical Bay, and frees you without coming onto you, then the achievement should unlock, provided you've seen the other scenes with the ladies shortly after being released.