You need to start a fight with pedestrians (or if a mission has about 5 people to use hand-to-hand combat on, that works) and hit A (360) or X (PS3) to do a dodge when they swing. After you dodge, hit Y/B (360) or Triangle/Circle (PS3) to successfully perform a counter attack.
In the middle of the night (I didn't check exactly what time, but it was around night/dawn), head South of your safe house onto the beach. Make your to the end of the beach under the pier (not a pier, but I can't think of the right word for it). There should be plenty of bums who can't fight very well.
You can easily counter a lot of their punches, and that is exactly what I did to get the achievement. There is also a Flying Rat (pigeon) on the beach there.