At the start of the battle against Vamp, he falls down after you getting his health low enough . As he gets up, grab him in a CQC hold and inject him with the syringe that you acquired earlier to disable his Nanites and make him mortal.
You do not have to deplete Vamp's health before CQC grabbing him. Instead, hide and sneak up behind him for a CQC.
Rather than depleting his life, use a tranquilizer gun and shoot his head. He will fall down, instantly giving you the chance for the CQC.