After talking to Mad Jack the first time, take out ARI and push . You'll see a blood trail that goes into the acid bath to Jayden's left. Take a look inside and Jack will hit you starting the first part of the fight. When you have the gun on him, select Impress as soon as you see it. When Jayden's nose starts to bleed, don't press . If you push the indicated button, you won't get this trophy. It says "fights", not "fight". This will trigger a new scene where Jayden is trapped. Go for the glove box to get the gun. Follow the QTE's to escape and in the second part of the fight.
Note: If you're going for "Nerd", make sure you find all of the clues before looking in the acid bath.
Replay Chapter: Mad Jack