A1: When you step off the elevator, three soldiers will be standing guard below. Do your best to approach them and take them out without being detected. Approach the door below with card 2. Inside is a prisoner who will tell you that Dr. Pettrovich is being held on the second floor. When you exit the room, the guards will return but they won't notice you for some reason. Run across to the right to reach room A2.
A2: There are two paths which lead down to the room below. Due to the arrangement of soldiers along the top, it's clearly easier to take the left path. Which ever path you decide, head south to reach room B2.
B2: One soldier guards the left path and two soldiers guard the right. Continue down whichever path you chose to room C2 below.
C2: A single jet pack soldier will be standing guard in front of the door along the bottom of the screen, which will open with card 4. Inside, you will find access card 5. Collect the card, exit the room, and head right to room C3.
C3: Another lone jet pack soldier guards the elevator. Take out the guard and enter the elevator. Inside will be another soldier. Run to the open door in the back to reach the actual elevator. This elevator, much like the previous one, is somewhat broken; it only goes down. Ride this elevator back down to the the first floor, and step outside.