Phase One
If you have two controllers connected into Port 1 and Port 4, press Z a few times on the Port 1 controller before the blackout.
Switch to Port 4 during blackout, and hold Z, right trigger and A.
If you want to use M9 for Mantis, R ◄ or ► 1 after Hideo Blackout
After dodging the psycho blast, wait until the vision becomes blurry to shoot Mantis in the head. Note the blurriness in the screenshot below.
After Mantis takes over Snake's view, release right trigger
THEN
Z.
This will cause Mantis to teleport nearby to the left. Headshot Mantis after he appears.
This will cause Mantis to teleport back into the original position. You can shoot him in the head before he appears.
After this headshot, move back behind Meryl, towards the door.
Aim for his right leg as he does the chair attack. His right leg (Snake's left) does just as much damage per hit as the head.
Remember, Mantis has invincibility frames, so do not spam the SOCOM.
Be careful of the vision take over as you finish Phase One