To play as the Cop, and thus unlocking this achievement, you'll need to bribe a cop three times.
Note that you cannot bribe more than one cop per level, but your number of bribes is cumulative over multiple plays through the game. You should be able to do this in one playthrough over three different levels.
You'll need $50 to be able to bribe a cop. If you're short on cash, you can loot the numerous trash cans, kill people and/or raid safes and treasure chests for extra cash,