Before attempting this trophy, make sure you've aced the Dominator and Smooth Talker skills. An aced Cleaner skill will also help but isn't necessary. Now for the actual mission.
The art gallery has three different entry points- the main entrance, a bathroom entrance on the right, and various skylights above the building. I personally used the bathroom entrance.
There will always be one guard at the front desk, he will glance back and forth- but will not move from this position. There will be four other guards roaming around the gallery- for a total of five. You can only answer 4 pagers successfully, so you need to intimidate (R2) the final guard and have him cuff himself. The guards roaming the gallery spawn in differently each game, so there really is no way to create a step-by-step guide for this trophy. However, some helpful tips are:
1. Bag the guards and throw them in a bathroom stall (front right of the building)
2. Never kill guards in doorways, wait until they have moved around a corner
3. Always kill the first four guards, the intimidated guard will be easy to for other enemies.
4. Don't shoot the cameras before you kill the guards unless you absolutely need to. While it's better to shoot the camera than to be detected, I failed this mission numerous times because the final guard saw a broken camera before I could deal with him.
After you've taken out the five guards, either melee or shoot the 4-5 cameras in the gallery. Once those are taken care of, bag the paintings with the red tag (there are a maximum of 9 of them, and some people have reported as few as six spawning in) and take them to the vehicle. With a little luck, you'll have nine paintings- which will net you the "Big Deal" trophy during the Day 2 mission.