I'm not entirely sure what exactly happened, because I randomly got the achievement. Best guess is that you should just mow a lot of lawns, and eventually the achievement will pop.
Update: As mentioned below by SPACE ODDITY, the achievement will only pop once you unlock the lawn mower and not the grass trimmer. You unlock the mower in a random job.
Update 2: According to Khost, you don't need to have the lawn mower. You can randomly get it while when you buy and sell a house after doing some work on it.