First as a note, if you are going for all achievements, I advise first getting 5 stars on all levels. This will increase your jump amount and limit the time we need to run the automation.

In order to automate this, you will need to set up a macro. This guide will be using a tool called AutoHotkey, which allows you to script custom macros with a great degree of flexibility. I highly advise checking it out and making your own macros for many other things, but at least for this grindy achievement, download AutoHotkey from this link: https://www.autohotkey.com/

After installing AutoHotkey, create a new ahk file anywhere you want, say, titled "aaaa.ahk".

Paste this into the file:

This script sets it so that when you enter ctrl + alt + k, it will begin executing a series of key inputs, repeating every ~4 seconds. It walks forward and to the right, waits, and then hits r to restart. Timers are used to make the delays asynchronous, so that at any time during the execution you can press "j" to cancel the macro. Remove the "^!" if your keyboard does not have ctrl + alt, which will just make the hotkey "k".

After pasting this in and saving the file, double click on the file to begin running the script. You can cancel the script by right clicking the autohotkey icon in the tool bar and selecting "Exit".

Open the game with the script running and enter the level "Just Breathe In That Honest City Air". It is on the opposite side from the starting level, above "Tip: Be nice to your pet mouse". After entering the level, hit ctrl + alt + k, then go do something for 4 or so hours. When you come back you will have the achievement :) Press "j" at any point to stop running the automation, you can restart the level and rerun it again afterwards.