You will find this on Level 8 - Advanced Research Complex. Towards the end of the level you will enter a large room (it has BFG LABS above the door you enter). You will see the BFG ahead of you and there will be multiple rooms here. The room to your left contains a torso that you can loot. This is used to open the room containing the BFG.
When you enter the room, it will detect you are not authorised to be here and will try to kill you. Jump above the BFG in the centre and on to any of the platforms at the side. When the lasers come down into the room, shoot the red bits on the bottom. After destroying some of these, the lasers will drop down and destroy the BFG container, allowing you to loot it for the trophy.
I am not sure if this is missable or not as I got it without trying anything else in the area in fear of missing it.