A lot of patience and careful shooting is required to get this. I did this on the first mission as to be able to not worry about being overrun with enemies. Note that the loot in the trunks of cars does count towards this, so try not to shoot at / near cars until you've looted them. If the car does catch fire, you do have a decent amount of time to still get the loot, just sprint towards the car.
For the loot in containers, the best way to find these is search the perimeter of every area, especially in areas that you can't see with the camera, other than ammo containers which light up blue, the containers can easily blend in with the environment. This will also help towards getting all the armor pieces, as these are very commonly in areas outside of the normal path of the level.