In order to get the final painting, you must do the Granny Rags missions to gain access to her other house and you must work with Slackjaw and go through with his idea for the nonlethal option.
Painting 1 is found during Mission 2 in Campbell's secret room. If he didn't go down there, it's all the way downstairs in his office. Press the eye on the statue.
For 2, 3 and 4 you will need to get the key to the Art Dealer's house and the vault combination in his house in Mission 3. The key is found on the body of a woman fighting two soldiers after the weeper alley area. She will give it to you voluntarily if you save her life. For the combination you first need to help Slackjaw get information about his friend from Doctor Galvani's house. He will then tell you about the safe and you can get the combination from the Art Dealer in the Golden Cat's Silver Room by torturing the guy. Painting 2 is on the second floor of his house, Painting 3 is on the third floor and Painting 4 is in the vault.
Painting 5 is found during Mission 4. It's in Sokolov's house, on the bottom floor, near the end of the mission.
Painting 6 and 7 are found during Mission 5. Painting 6 is on the second floor of the house in the art gallery and Painting 7 is found in your target's room (the locked one, a guard nearby has the key).
Painting 8 is on the second floor of the tower in the Music Room, near the Regent's Bedroom.
Paintings 9, 10 and 11 are found in the very long Mission 7. Painting 9 is in a room with a balcony not too far from the rooftop overlooking the door leading to Daud's area . Painting 10 is on a level partway down the chain after you deal with Daud. Painting 11 is in Granny Rags' second house, see the note at the top of the guide.