Approach this front from the north. There should be a brick wall to your left and a green pickup truck beyond that. Crouch behind the truck and take out the Tattaglia ahead. Then go up the steps with the burning barrel on it. When you reach the top, go through the doorway on your right, then turn left and go down the hall. There will be a door to your right. Take cover to the right of the door, then open it, and shoot at the enemies inside. Go through the doorway, turn right, and crouch behind the furniture and boxes ahead, and kill as many enemies as you can from there. Then run up to the right of the large entranceway, take cover, and battle from there.
When everyone is dead, go into the room and go behind the bar on the right to find the hidden moneybags. Now go back out of the room, go into free-aim mode, and destroy the tall wooden crates blocking your way ahead to the right. Once you do, a Tattaglia will run out so be ready to kill him. Now go down the stairs that you've just gained access to. When you reach the bottom, turn right, take cover to the right of the open doorway, and kill the Tattaglias in the next room.
Then, take cover to the left of the double doors to your left, open the doors, and kill the enemy in that room. Then creep slowly into the room until there is an explosion then quickly take cover behind the bar to your right. Kill the rest of the enemies from there. Make sure at least one of the windows' glass is completely shot out, then plant the bomb and vault through the open window.