This part is a little tricky. From the start of the level, there will be 4 guards, 1 directly in front of you that paces, 2 in the room to your right, and 1 down the hall on the balcony. Right when you start, walk forward a little and take cover to your right. Wait until the guard in front of you walks to the right and dash across the hall into cover. You should be right next to an open doorway with a guard leaning against a table. You have to do this part quickly so the guards in this room don’t see you. Walk down the hall while crouched and when the guard on the balcony leans over the railing, go to the left and jump over the rail so you are against the wall. Once you get across to the next balcony, immediately run into the room and take cover against the shelves directly in front of you. There should be a guard coming out of the room on your right and walk across the room you’re in into the room on your left. Once he passes you, move out of cover but stay crouched and go into the hall. Go to your left once in the hall and crouch against the wall. Slowly walk forward and the guard in front of you will walk down the hall. Go into the room straight ahead and take cover on the wall on your left. Wait until the guard moves back down the hallway to your left and quickly go out the door and press X against the cart to move it. Run into the room and go to the left. There is a cart in the middle of the room and you have to go up to it and press X. Stay crouching while doing this so the guards don’t hear you. Once you move the cart, press the Back button to see where the guard outside the room is. Once he passes the room going either way, go up to the cart and climb up. Walk across the shelves and there is a vent above you. Press X to open it and then press Y to jump into it.
If you alert a guard, just restart from the last checkpoint and you will still unlock the achievement.