This trophy is obtained in Act 2: South America. You need to defeat the beast for of Laughing Octopus with non-lethal means, which means to need to deplete her psyche gauge instead of their health gauge by using CQC, sleep mines, Mk. 2 pistol, etc. Her psyche gauge is the thin bar with four sections under her health bar.
The easiest way to defeat her is to make sure you're using the Solid Eye's night vision mode (L2 and square when the Solid Eye is equipped) as she has stealth camo. She will shoot at you and then she will hide in various places. If you use night vision though it will make her extremely obvious when you find her. After the battle she will shed her suit and walk after you, before you attack her again run around and look on the beds, the Laughing Octopus doll will be on top of one of them, pick it up to get the trophy.
As a side note, after she sheds her suit, if you continue to tranquilize her you will get her face camo when the battle is over, which will count towards:
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