This takes place during the trial of The Lost Turnabout (JFA/Ep.1).
Detective Gumshoe will take the stand, but you'll have to wait for his second testimony: "Dustin & Maggey".
As stated in the trophy description, you'll only need to "Press" the second statement: "It sounded like they were even talking about marriage."
Eventually during questioning, Gumshoe will blast out "Mind Your Own Business, Pal!" and that should unlock the trophy.