You will have to patiently wait for this platform to reach the end of its journey. Perform a single jump towards a well know balcony. Pull the lever. Once this is done, activate either a slow-motion or a time stop feature. The objective here will be to go back to the moving platform. You must wait for it to get to an opposite balcony. Save the game there and begin your exploration.
You can decide to call an elevator and you could try and get down to the lower level on your own. Either way, you will have to explore this area. Head on to a small assembly line (screen). Once again, you must use one of your abilities. Activate a reverse time feature and perform a jump towards the assembly line. Make sure that you're crouching here. If you've done everything according to the plan, you should be able to reach a new room. Leave the assembly line before your suit runs out of power.
You are going to be attacked by a small group of enemy soldiers. I'd strongly recommend hiding to your left. Wait for one of the soldiers to get here and kill him (screen). Next, deal with the remaining two. They will be occupying some of the upper balconies.
Make sure that the area has been secured. Leave your cover and head on to the stairs (screen). You won't have to perform any unnecessary stops here. There's also only one passageway here, so you can't get lost. You will eventually reach some of the upper balconies. Perform a jump towards the pipes, because that's how you'll reach your next goal area.
Use the pipes to move forward (screen). After that, you will have to turn left, because there's an entrance to a small ventilation shaft here. Use it. I'm sure that you won't be surprised by the fact that you have to jump down. This will allow you to proceed with the next mission of the game.