my favorite way to get up that stairway is to just keep tossing Stun Grenades and running. *i hardly ever have to kill anyone that way. *the soldiers behind me never get close enough, and the ones on the stairway are just lying there as Snake jogs by. *once in a while i stop at the top floor before the ladder and take them out one by one as they're catching up, but it's not so good if you're going for a good grade to be killing soldiers.
and yeah, Fox Die is right. *the Body Armor is one of the doors in the area that had the electrified floor and poison gas.