It's better to go for this on your good playthrough because the karma bonuses you get from them will help towards getting full positive karma. When you're running around the streets of New Marais, street crimes will occasionally take place which you can choose to ignore or complete them for some quick XP and karma based stunt bonuses. Completing crimes represented in blue will lead to positive karma boosts.
Street crimes range from:
Complete 80 of these crimes to unlock your trophy. Because these crimes occur at random, there is no real way to grind these other than running around town until they occur. That said, make a habit of doing them during the course of your story so you don't have to grind for these later.