On this page of our guide to BioShock Infinite you will find the first part of a detailed walkthrough of Chapter 4 - Comstock Center Rooftops. Booker must head towards the Monument Island. The main character will meet the Lutece siblings again. Also, you will be able to use hooks to reach remote ledges and platforms. The hero will acquire a new weapon that may be useful to eliminate dozens of enemies - a machine gun.
As soon as you've entered the The Blue Ribbon Restaurant you should turn around. Check the area behind the counter and open a locker. Notice three kinetoscopes at the end of the hallway leading to the main area of the restaurant. Use each kinetoscope in order to unlock Vantage Points #5-7.
Once you've entered the main area you'll encounter the Lutece siblings again. Before you approach Rosalinda check the tables and the area behind the bar, finding coins, a wallet and some money in the register. You may now take the gift from Rosalinda and it's a new Infusion named Shield. From now on you'll notice a new bar under your health meter and it will inform you about your defences. The shield goes down first and it can regenerate on its own when you're not under attack.
Proceed towards the kitchen. Obviously you can find some food and alcohol here, however you should also search the area for Voxophone #6. Find the kitchen exit.
Proceed to a balcony located behind the restaurant and look up, centering the view on a red and white building hovering nearby. Aim your Sky-Hook at one of the nearest hooks and wait for it to start glowing green. Make a jump and the Sky-Hook will attach you to the hook of the wall, allowing you to travel between unconnected buildings.
Continue using the Sky-Hook to connect to nearby hooks until you get to the last one. You'll now have your first opportunity to perform an airborne execution. Make sure you're attached to the last hook and aim at a policeman standing on a nearby roof. Jump towards the policeman as soon as a yellow marker will appear under him. Performing executions will allow you to kill most enemies with one hit.
After you've landed check the crates in order to collect a Machine Gun along with some ammunition. Continue moving towards your current destination.
A police barge with a mounted turret is hovering near your roof. You can destroy the turret or use possession on it, however don't forget to deal with policemen heading your way. Keep moving, exploring a small room along the way (salts and several containers).
Another police barge can be located on the other side of the roof and two more will arrive soon, both with police reinforcements. I recommend possessing the turret, because it will help you to deal with the remaining enemies.
After you've won the battle (or avoided it) head down to a lower roof and locate a skylight in order to enter Lansdowne Residence. Explore the attic thoroughly before descending to a lower floor.
The first floor of the residence contains a bedroom. Check this room to find some interactive pieces of furniture and ammunition. There's a Voxophone #7 on one of the shelves of the dresser and an ornate chest. Examining the chest will allow you to start a side mission entitled Find the key that fits the lock (it's described at the end of this chapter).
Proceed to the ground floor. You can find some salts here, a silver tab and several other things. When you're done exploring return to the top floor and head to the balcony.
You can use a Sky-hook to travel from the residence balcony to a nearby terrace. Check the garden area under the umbrellas and open a mailbox. You may now enter a printing house.
Once you're in the main area of the printing house you'll probably notice that police reinforcements are trying to get in. Quickly use the corridor to travel to nearby rooms, because otherwise you would start the battle in a bad spot. Stop in a room with a fireplace. Check the area near the door to find a machine gun and salt supplies.
Use the back door to leave the building and expect to be forced to engage a new group of police units. Notice that your enemies are accompanied by a Fireman and there's also a turret above the battlefield. Use possession on the turret and then eliminate all hostile units so that you'll be able to explore this area in peace.
Use the stairs found behind the Dolar Bill machine. Explore the area behind the wooden shed to find Vantage Point #8: Kinetoscope.