This mission is all about timing. And depending on how much patience you (don't) have, you might want to sedate or kill a guard and take their disguise instead of going for Silent assassin here.
Starting this level
You start out in the elevator. While walking, turn right 180 degrees and then, once the door straight ahead closes, run left. Look through the keyhole and wait for the guard to walk all the way out of sight, as soon as that happens walk, while hugging the wall to the left, to the room with a spare keycard inside. Pick the lock, take the keycard and run back to where you came from. Hide by the plant on the right side, while sneaking.
Luring the admin and first objective
Once the guard disappears, make your way to the air conditioning room. This is the door with the red keycard reader, unfortunately the spare keycard won't open the yellow door where you'll need to be. Shoot the bar above the "Temperature: Normal" sign and stay in the room until the system administrator runs to the computer room. Once he is inside, sneak in and hide behind the wall to the right and wait for him to leave. Once he moves out of your sight, run to the computer and plant the hacking device.
An alternative way is to lure the admin away from his room so you can take the spare keycard on his desk. This can be done by shooting any of the computer screens in the three office cubicles rooms that say they're running an active program. This can be done without alerting the nearby employees depending on the computer and so is making your way to the admin's office. Be careful of the patrolling guard however. Make your way back to the yellow keycard door and plant the hacking device. This is a longer process than the previous method and will still take one bullet, so the method above is advised.
Leaving this level
Leave the computer room and go to the corridor to your right. Sneak past the guard and hide by the lamp on the right until he turns around. Look right and walk to the double doors on the left, and look through the keyhole. Wait for the guard to pass and sneak past him, then start walking. Once you make your way out, run left, but wait for the corridor to be clear of people. Before shooting the glass to the right, make sure the guard nearest to you starts walking left. Watch this video from 7:18 and on to help you for this part. It is very difficult and requires near perfect timing.