For this trophy to pop you need to have all 3 Shotguns on display in your shed. None of the Shotguns are concealable. See All Firearms Collected for an enhanced explanation for collecting weapons.
Shotgun (0:51): This can be found in the Mission 1: Anathema. Make sure you are armed with the Silver Ballers SD, you also want to get the Mansion Guard disguise as this will make getting this gun easier. Complete all your objectives before you get the Shotgun. The Shotgun can be found right at the front of the villa, there are two guards so you are going to have to kill both of them quickly. One will have the Shotgun, pick it up and you will see another guard walking over to investigate. Kill him and extract via the car.
Sawn-off: To unlock this you need 2 consecutive Silent Assassin Ratings. These can be achieved by either doing 2 different missions or doing the same mission twice with a Silent Assassin rating.
SP 12 (1:56): This can be found in Mission 16: Temple City Ambush. Due to the shotgun not being concealable; complete all your objectives and then backtrack to the carpet shop where you meet your first contact at the start of the mission. Take the Shotgun and extract. Keep to the back streets and do not return to the town's main squares, otherwise you may be engaged in a gun battle.
Just got the SP12 in Temple City Ambush. I already got the regular Shotgun from the beginning and the Sawn-off as well. The trophy is still yet to pop. Do I have to wait to go back to the shed in order to get the trophy?