To unlock the Prohibition trophy in the Turf Wars DLC, you need to take down the four Hammerhead gang hideouts that appear on the map. They will all become available after you complete the second story mission "The Bar With No Name". They are all relatively straight forward, however things can get quite tight with a combination of whip-wielders, heavies with mini-guns, jet-packers and a metric tonne of missile launchers. Just make sure to take your time and always be ready to dodge and you should be fine.
Once you have completed all four hideouts the trophy will be yours.