2nd EDIT:
It appears this achievement is also bugged at the moment and cannot be unlocked (thanks to erod550). Some people have been unlocking this achievement again, but it looks like you will need to do a new playthrough in order to unlock it, otherwise it will stay locked.
There are a total of 18 Racket Bosses in the game, however 2 of them cannot be flipped - they will die no matter what. These are the Prostitution Racket boss (the very first one in the game, before you're taught how to flip Bosses) and the Slavery Racket boss (for kinda obvious reasons.)
In order to flip the 16 Racket Bosses for the achievement, you will need to have the area they're in wiretapped. You can check on your map if an area is wiretapped by clicking on
, which will light up the areas in the district that are wiretapped. When you go to confront a Racket Boss, assuming you have wiretapped the area, you will get the option to either kill or recruit him. RECRUIT him
, as killing just one of the bosses will void the achievement for the playthrough.
The achievement should pop as soon as you flip the 16th Racket Boss, assuming you've recruited all available ones.
EDIT: So to avoid some confusion, you should know that each district is divided into a number of areas. You only need to wiretap the areas where the final confrontation with the Racket Bosses occur. You do NOT need to wiretap the entire district.
As a sidenote, I missed this achievement on my first playthrough because I forgot to wiretap an area before going for the Racket Boss, but when I went back and recruited him on my 3rd playthrough, the achievement popped. Whether this is a bug or if you just need to flip all the bosses once across all playthroughs I'm not willing to guess.
Slimey Cat Log says: "I can confirm that the playthroughs carry over. I got the achievement on my second play through on the third racket boss." which would appear to back up the idea that the bosses only need to be flipped once across all playthroughs.