To unlock The Long Con trophy in Spider-Man The City That Never Sleeps: The Heist, you first need to find all the stolen paintings that appear on the map after you have completed a couple of story missions.
These are pretty easy to track down and are normally on the roof of the building, although in one case it's in the subway tunnel below and in another it's on the side of the building. You'll get your ping tracker that you normally use for finding kidnapped people in car trunks in the main game. As you approach the area you want to scan the environment and find a glowing yellow environmental object, then pull on it to reveal it as a fake and retrieve the painting.
Once you have tracked down all of the available paintings a final painting will appear on the map. Find that one too and after a couple of conversations a Side Mission will appear. Go and resolve that quest (just go to it, basically, and listen) to finish the quest line. This trophy will unlock shortly after the conclusion.