See Youth Trumps Experience for more info.
This achievement is the exact opposite of Youth Trumps Experience, so you have to take a much different approach. Marburg respects those that are loyal, and finish what they start. That means, use nothing but Professional responses with him.
Eventually, when you get to the mission "Intercept Marburg at the Museum of Art", stick yet again with Professional answers before the boss fight. After you've damaged him enough, he will talk to you yet again. Simply stick with Professional answers again, and he will retreat. After that, the achievement will unlock.
WARNING: If you plan on getting this achievement, make sure that you decide to disarm the bombs. Even if you get Marburg to like you, you won't get this achievement by saving Madison. As such, follow the Road Map strategy, and make sure you go for the bombs.