If you want this achievement as soon as possible without worrying about keeping it for your FOB, or getting it stolen from your FOB, do this.
If you are NOT connected to the internet, skip to the bottom.
- As soon as you get the DETERRENCE trophy, if you go to dispose of your nuke, you may get an error message. This is because it hasn't been transferred to your FOB.
- Press your PS button on controller.
- Settings -> Network Settings
- Uncheck connect to Internet option
- Back on the game you should get a message about being disconnected from the network.
- Open iDroid, Resources -> far right tab, Dispose.