Instructions
Place a fully loaded assault rifle and syringe in your active items before the fight starts. Inject yourself with the syringe. Press "L2" and "X" on the PS3 controller to inject yourself. The syringe will prevent Screaming Mantis from reading your mind. Look at your psych gauge often to see that it is blinking. She will be able to read your mind if it stops blinking. Inject yourself with the syringe once your psych gauge stops blinking.
Run to Meryl and hold her by pressing the "R1" button. Press the "Triangle" button to inject her with the syringe. This will break Screaming Mantis' grip on Meryl, make her faint and fall to the ground.
Kill all of the "Ghost" Frog units that are hovering around the room. Screaming Mantis will resurrect them occasionally. However, killing them will remove distractions so you can focus on Screaming Mantis.
Find Screaming Mantis. Go to the middle of the room and equip your assault rifle. Screaming Mantis will be hovering above the holographic globe. Start by shooting the little dolls hanging from her hands. After a few shots, Screaming Mantis will float to Meryl and revive her and force her to shoot herself. Run to Meryl and inject her with the syringe again to make her stop. Screaming Mantis will now fly across the room.
Run to Screaming Mantis and keep shooting her puppet dolls. Grab one of the puppet dolls as soon it falls to the ground otherwise Screaming Mantis will resurrect it. It will take about four or five shots to knock a doll out of her hand.
Equip a puppet doll in your weapons box. Aim the puppet doll at Screaming Mantis to release its soul. Hold down the "L1" button until the doll's soul engulfs Screaming Mantis and kills her.