Take the bugged painting into Dimitri's office and swap it with a regular painting without getting hit.
How to CompleteEdit
You must sneak a bugged painting into Dimitri's office. To enter, head through a window which can be reached by climbing up a drain pipe. Be careful when going past guards on your way because you must keep the painting safe. If you get a guard's attention, run away from the guards quickly before they attack you. If Sly gets attacked, he will drop the painting and you will fail the mission.
Once inside, approach further through the nightclub. Sneak past the janitor rat guards, who will attack you if they spot you. Remember to be careful on fighting them as you must still keep the painting safe. Make your way over to the red lasers. Avoid the lasers by jumping onto the piano and climbing up a golden spiral pipe onto a red ledge, and sneak across the wall to the next ledge. From here, run across the rope that leads to the opposite wall and crawl under the waterfall. You can then smash open the vent and crawl through.
After crawling through, you will land in Dimitri's office. Switch the paintings, and the job is completed.
It is not necessary to get the original painting back to Bentley in one piece, but you will be able to get a lot of coins from it through ThiefNet if you do manage to return to the safe house with it.
After entering the nightclub through the window and hearing Bentley's info, follow the guard making a circle at the bottom of the stairs. Follow him through the hallway on the right until you are out on the other side. Afterwards, continue up the several steps and over the lasers. Then, follow the instructions above. It is less risky and more quiet following this method. Less of a chance to be involved in open conflict.