I'll try to explain this achievement because the game doesn't exactly explain rackets-attack and enforcers-killing very well.
Some time into the game, you'll start getting missions to attack rackets. These rackets usually take the form of illegal businesses like prostitution, contraband, union extortion, etc. To initiate an attack, you'd first need to speak to a contact. Once this is done, several icons will appear on the map. These icons are the locations of the various establishments forming the rackets.
To attack a racket, your task is to cause enough damage to these establishments, until the racket boss appears in the main warehouse. The damage required differs from racket to racket. It usually ranges between $20,000 to $30,000 per racket during the earlier missions, but may go as high as $100,000 later. To "damage" a racket, you'd need to go to the locations where the icons are, and start wrecking havoc. Again, the tasks you need to do varies from racket to racket. You could hurt them by stealing money, helping prostitutes escape, stealing medical supplies, destroying contraband items, and killing enforcers.
To unlock this achievement, you'd need to ensure that in the process of dealing damage to a racket, you never, ever kill an enforcer.
These enforcers are easy to spot - their locations appear on the map as some sort of a skull/ alien icon. To be safe, I'd suggest never even approaching these locations at all. Focus on dealing damages at other icons instead - there's definitely enough things to do to deal sufficient damage to force the boss out without killing the enforcers. You can kill all other enemies, just make sure you don't kill these dudes. They also have the word "KILL" above their heads to make it easier for you to spot them.
Note: Always use the
button to use "instinct", Hitman-style, to spot the locations of enemies during fights. This makes things so much easier. Instinct also usually points you to your objectives, show the locations of medical/ weapon cabinets (so that you can refill), locations of money to steal, etc.
Once you deal enough damage to a racket, i.e., reduce the required amount to $0, the racket boss will appear in their HQ. Go talk to your contact to launch a final attack on the racket. Select
to accept that all undone missions in this racket will be forfeited forever, and the achievement will unlock. Yes, you don't even need to take on the boss. The achievement will unlock before you head to the boss fight.
PS: Do note though that enforcers that are not killed during the earlier attacks will appear at the HQ to make the boss fight somewhat harder. Also, it'd be better to try to get this achievement done in the earlier rackets, because the later ones are much harder to do. One later mission has as many as eight enforcers - you won't want to spare them before going to the racket boss.