Dishonored Death of the Outsider has 8 Painting Locations. Finding all Paintings unlocks the Art Aficionado trophy or achievement.

All of the painting collectibles are found within the first 3 missions. Painting #6 requires you to do the side quest "Sedate the Bank Personnel". Everything else is found in main mission areas and doesn't require special keys or anything extra.
You have to get all paintings in one run! If you miss one and move on to the next chapter you'd have to reload a previous save game to go back.
The good news is that within their respective missions you can get them at any time, even after completing the main objectives. Some paintings require a little bit of progress with the main objectives.

At the end of every mission you can also see how many paintings / bonecharms / coins you have discovered.
The collectible progress is only saved when you trigger an auto-save or manual save. If you die without saving you have to pick them up again. Its best to save manually after every collectible.
The Paintings also give you 200 coins each.

TIMELINE:
#1 - Mission 1 - 0:05
#2 - Mission 2 - 0:26
#3 - Mission 2 - 1:00
#4 - Mission 2 - 1:37
#5 - Mission 3 - 1:58
#6 - Mission 3 - 3:00
#7 - Mission 3 - 5:10
#8 - Mission 3 - 6:53