This trophy is unlocked after the boss fight of Chapter 3: O'Bannon Farm.
The fight itself is in three separate stages, and during this fight you can also earn the trophy:
During the first stage, she will be in the center of a circle and launch bubbles at you. Simply continue moving around the circle, shooting your Blaster and strafing her, and if necessary jump out of the way of the balloon/bubble attack. You will know if you get hit as Juliet will be trapped in one, and the game will prompt you to repeatedly press O to get out.
During the second stage, she will split into four. This is basically the same fight as the first stage, except you will also have tractors coming at you from both sides, and she will have a mechanical arm coming from the center. You can take damage from both tractors and arm, but if you want The Third Eye trophy, continue to avoid her balloon/bubble attacks.
During the third stage, she does not use the bubble attack, and a hand will attack you on the platform you are on. This is the easiest stage, as you can simply run from the hand and continuously shoot the six versions of her in the center. Just remember to dodge the bubble attack she will throw at you as you make your way to her during the final cut.
The trophy will unlock after the fight. If you are going for The Third Eye trophy, it will unlock here as well.
Below is a video to help, and all credit goes to Swrinny.
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