Champion requires you to win fist fights. It may help quite a bit to do this after you've unlocked some of the Assassin Techniques because one of them gives you more time to react during a fist fight.
The best maps are King of Chinatown or Welcome to Hope. I prefer Welcome to Hope because the people in the bar will approach you rather than run away from you if a fight breaks out.
Simply walk up to anybody and hit the X/Square button to start a fist fight. Just be sure to approach from the front so you don't just knock them out. Complete the Quick Time prompts successfully to win the fight. Do this several times in a row to unlock this Play Style.
