As you play, trash will appear on the ground, you will have to take a broom and click on the trash. This will clean the trash up and progress towards the achievement. You will need a total of 200 pieces of trash cleaned. There isn't really a way to speed this up other than playing the game. You can check your progress on the Managers Blackboard under the Statistics tab. Once "Total Trash Collected" hits 200 you are good.
It is worth noting that the cleaner robots that you can purchase do not help you progress towards this achievement. You have to manually clean 200 pieces of trash.
The achievement will unlock after you close the store for the night after you clean your 200th piece of trash.