There's no easy way to get this achievement -- it's an annoying timesink. After playing through the game in normal and hard mode as well as getting A+ rankings on all normal levels, I only had ~34,000 kills. To get the last 16,000, I did what everyone else is doing and started farming the first floor of First Blood on Hard Mode. More info about the run below!
A few things regarding the strategy:
I originally tried a strategy that cleared most of the floor, but this only netted me an average of 5,000 kills per hour. Once I switched my strategy to only focusing on the first group of enemies and then immediately restarting, I reached a peak rate of 7,608 kills per hour. To recreate the scenario seen in the video, rewind the level until the guard with the gun has a pump shotgun (easiest to dodge and avoid with door flipping) and a knife-wielding thug patrolling right next to the gunman. The positioning will make it so that even if you knock both the gunman and the knife wielder out simultaneously you should always grab the knife instead of the shotgun. I prefer the knife because it has the fastest swing time. Once you get the rhythm down you should be able to average 6-8 kills per pass.
Checking your kill count:
If you're running the PC version, you can actually check your kill count by navigating to the following directory: Documents/My Games/Hotline Miami 2. Once inside the directory, open savedata.vfs in a text editor and search for "achievements/achievement 17" -- the value next to this achievement is your current kill count.