In the first part of the battle against Vamp, after you get his health low enough he falls down. As he gets up, grab him in a CQC hold and inject him with the syringe that you obtained earlier. This will disable his Nanites and make him mortal.

You do not have to deplete Vamp's health before CQC grabbing him. Hide and sneak up behind him for a CQC.

Instead of depleting his life, use a tranquilizer gun and shoot his head. He will fall down, immediately giving you the chance for the CQC.