Dispose 150 bodies in your car or body drop locations in order to get this achievement. You can easily grind this achievement early on if you want to get it out of the way, but it can be done at any point. I highly suggest completing the campaign as a majority of your count will come from this (I had about 20 to grind after I got done with the campaign).
You are not required to finish the level so you can simply grab a couple bodies and dispose and hit Restart (which will restart the level).
I chose Contract 2 because you have access to 3 bodies total, 2 usually being pretty easy to get and only have to deal with 2 cops. 1 body will always spawn in the courtyard and 2 will spawn in the gym. The easiest setup is when the 2 gym bodies are closest to the gym office and NOT in the ring or in the outside corners. If I got those layouts, I typically just reset for the simpler layout which will give you 3 of 3 bodies instead of one quick one.
Dispose 150 total and the achievement will unlock a few seconds after!