You'll be able to get your first opportunities of starting your own battles in chapter 3, when you have the possibility to explore downtown without being restricted to a mission.
In order to initiate a fight yourself, as you're walking around the place, you'll notice EVERYBODY is moving, but time to time, you'll come across a person who is stood still, not doing anything. Don't get too close to him, or he'll run at you, what you do is press in the Right Stick to go into first-person mode and look at the person for a second or two, it doesn't activate INSTANTLY. If it doesn't work then that means you're too far away, Simply just come out of first-person move a step or two forward and try again, eventually when you get it right, he'll come running at you instead, and say something about you looking at him in one way or another.
Don't go running straight at the person before using first-person, because if you get too close then he'll decide to run at you, not counting towards the trophy as you're not in first-person.