Follow Elizabeth to the cemetery and break into Lady Comstrock's crypt. Open the coffin only to realize too late how bad an idea that was. This will be the first of several encounters with the Siren. Keep in mind that she revives the dead so the only way to end the encounter is to kill her. Hopefully you brought a gun with plenty of ammo reserves (like the Machine Gun or Burst Gun). The "zombies" do drop ammunition constantly however so ammo shortage is not really an issue.
One way to keep the Siren "solid" long enough for you to shoot at is to kill "zombies" that are near you, so she comes over to revive them. Deal as much damage as you while she's trying to bring them back to life. If you're going to use Vigors, avoid Murder of the Crows as she is immune to it.
There is another crypt opposite to that of Lady Comstock's with a piece of Gear in it. Open that one by igniting the pair of torches at the gate with the Devil's Kiss. Head for the cemetery's exit and receive an objective change from the Lutece twins -- find the three tears
For the first tear, follow the phantom trail to the Luteces' laboratory in the Market District. Kill the goons outside first and pick the lock open. There is a Voxophone in the room adjacent to where the tear is. Visit the bed room upstairs next for an Infusion phial plus another Voxophone sitting on the floor between the bed and the night stand.
Go back downstairs now and open the tear. There should be a Voxophone on the ground where the tear used to be afterward, so don't forget to pick it up.
The second tear is inside the Bank of the Prophet. Kill the enemies that come puring out of the door including a Crow then take the elevator to the Main Hall. You will encounter another wave of hostiles so go clean house. Once the area is clear, take a left at the vault and enter the other door in the next room. There, the Code Book comes into play in the section that says "HOARDER" on the wall. Use the typewriter to open a secret room full of valuable loot.
Take everything in there including the Infusion and Voxophone after which you can return to the vault and go the other way. Follow the objective marker to a fork where you should go straight to the end of the room to score a piece of Gear next to the corpse. In the room with the tear (Book of the Prophet), turn left and collect the Voxophone on the ground behind the safe.
Head to where the tear is, kill the Crow, open the rift and grab the Voxophone that appears in its place. The Siren meets you as soon as you the vault so be ready.
Once again follow the phantom trail or better yet the objective arrow to the photography studio for the third and final tear. Open it and retrieve the Voxophone that pops up. Before returning to the Comstock estate, check your ammo reserves; make sure you have plenty for the big fight ahead.
Defeat the Siren then enter the house. Blood in the Streets achievement / trophy unlocked.