The tutorials that appear right before you grab your gear are informative to this achievement. You can read them later in the pause menu or read about it here so don't worry about missing them.
This works like a kill streak. You have to kill 4 enemies in a row without being detected. This includes putting enemies on alert without having them see you. Any stealth kill will work so I recommend finding silenced weapons that are scattered along the route. Throwing knives are also good but often Chain Take Downs are the way to go.
Your streak is lost when you die or when you are detected. Each step in the streak gets you a perk activated. The first one is quicker movement when crouched. To see how many steps you've done in the chain, checkout the 4 circles above your crouch symbol in the bottom right of the screen.
It's fully cumulative so if you kill 5 guys in a row so it IS possible to do this in only 29 kills. However everytime the streak resets it will require another 4 to build it back up.