***UPDATE***
This game, and therefore all of its achievements, have been discontinued.
***OLD SOLUTION***
From the waypoint, go to Patrols and then Midtown Patrol.
There are two to three villains around the area naturally (shown in little bubbles) - Black Cat, Crossbones, and Man Ape.
However, you'll likely spend a lot of time on the timed events that happen every few minutes. This will be groups of three to five villains that most others in the Patrol will also go fight, and it's a good way to gain experience and loot items.
In between, you can also work on saving citizens for the related achievement.
After 150 villains are defeated, it pops!