Bioshock Infinite Walkthrough Part 35: Guns For The Lady (Finkton: Good Time Club to Shantytown)
As Booker emerges into this alternate Columbia he can grab a Vox Repeater, a burst fire version of the Carbine. Head on out of the room and turn to the left. Look on the table just outside the storage room you arrived in to find a lockpick hidden behind the crate on the table. After that head on up the stairs to the entrance of Cell #9. You will pass one very full cell of Vox Populi. After that continue on up the stairs.
You will find the cell block is a lot more full here. There are a lot of Vox imprisoned here and they seem to be clamoring to get out. Head on through the cell block and into the room with the interrogation video. You will see it too has changed. Mr. Lin was set free because of his wife's connections. Just continue on through, going up the stairs. You will find your way back into the storage room. Close to the exit you will come across the 2 guards you killed there. They are flickering some, as those 2 realities are too close and are contradicting one another. You can either let them be or kill them a second time. Head back on through the dressing room and up into the Club itself once again.
Once inside the club itself you will find a large number of Founders coming after you. Fink will be yelling at someone about you just appearing in the basement of this club. Get into cover, if not onto the balcony above, and take out the all the Founders who are coming at you. When the fight is over, loot the bodies then head up to the balcony, if you are not there already, then go on through the door toward the entrance of the Club. When you cross into the entrance hall, look to the right of the Minute Men Armory. You will see a Kinetoscope: “Gunsmith Set Free”. There are a number of different Voxophones and Kinetoscopes now. Watch that, grab any upgrades you want from the Minuteman's Armory and then head outside. Quite a bit has changed so it is time to deal with all that.
Once outside take a moment to equip Possession and one of your offensive vigors (Like Murder of Crows or Devil's Kiss). Head over to the left through the open gate, as the path to the right is sealed off. Now head through the gate carefully and throw out possession at the nearest of the soldiers. Just fight your way through them all and over to the right. There are not big surprises beyond a Beast with a Volley Gun and a few Gun Automatons. All of those are easily dealt with. Simply hit them with Possession and they will take care of your enemies easily. You may need to kill the Automatons but that is nothing too bad.
After the fighting head into the Gunsmith's Shop. Things are looking good as it is not thoroughly trashed anymore. Head inside the Shop itself and go on up the stairs to the top floor. There you will find Chen Lin in that same fuzzy state of being the 2 guards were in. He will not be too cooperative so head back down to the shrine. Talk with the woman there to learn what is going on. She makes it clear she is Mrs. Lin. She will ask you to go get Mr. Lin's tools back from the Impound in the hope that letting him work will help him come back to normal. This means you need head into Shantytown town to get it back.
Head outside the Gunshop and over to the left toward the entrance to Shantytown. A second wave of Founders will come after Booker and Elizabeth. Use Possession to quickly deal with them and any other vigors that are handy for a few Founders. Once they are all dead then head through the double doors leading to Shantytown. If you have not claimed the cache inside the Clocksmith's Shop to the right of Shantytown, then this is a good time to do just that. Head inside the Clocksmith's shop and use the code book. Interact with the clock to the right of the code to find a Voxophone: Vivian Monroe "A Truer Allegiance", a Volley Gun and an Infusion.
. Just inside, to the right, you will find 2 Vending Machines (Dollar Bill and Vigor). Opposite the Vending Machines you will find the lever you need to pull to gain access to Shantytown. Do so and head through. Just remember you will need to pull another to get back.