On this page of our guide to BioShock Infinite you will find the second part of a detailed walkthrough of Chapter 21 - Shantytown. Booker and Elizabeth must win the large battle. In addition to the usual enemies, they have to deal with two rocket turrets and a Patriot. Our walkthrough describes different variants of winning the battle depending on the chosen level of difficulty and weapons used.
Before you'll be able to enter the police impound you're going to have to defeat a small group of policemen. The police units will be supported by two rocket turrets, one machine-gun turret and a Mechanized Patriot. The best way to handle this challenge is to remain on the balcony with the telescope. The balcony is large enough to move around freely and it offers a lot of cover against the enemy fire.
Besides, enemy attacks shouldn't be such a big problem from this distance. The sniper rifle you've found here contains enough ammunition for you to destroy all the turrets. If you're playing on a normal difficulty setting each rocket turret will explode after receiving eight hits from the sniper rifle. Elizabeth should provide you with additional ammunition and you can use it to get rid of the policemen and the Patriot.
If by some chance you prefer short distance fights, then you should take some time to find Grenade Launchers (on a building in the right side of the square and on a roof of a barge to the left) and Volley Guns (on top of the building to the right).
You can also open a tear located near the left building (it contains one more sniper rifle) or above the entrance to the police precinct (it summons a Mosquito). Use the sky-lines to travel between buildings, using this opportunity to eliminate enemy units while moving.
If you encounter problems with your health, then you should open a tear located close to the right building, because it contains medkits. Finally, there's a shooting range behind the left building and you can summon a machine with rockets.
Once you've eliminated all enemy units use the sky-line to get to the back of the right building. Collect Voxophone #44 and enter the police precinct to end this chapter.