There are 2 ways you can complete this achievement.
1. If you have completed most other achievements and only one or two remain that won't take too much game time, you can go to the music folder and delete all songs in the folders but keep a song that only takes 15-20 seconds (you can view this in explorer). Now copy this song to all other folders. Your listening count will keep going up as you complete your other final achievements.
You can keep the game AFK too but remember, it will take around 55 hours (if starting from 0) to complete the achievement. This method is best used when you are completing other achievements. I suggest using this method when completing the 'Wrench master (Gold)' achievement. (Please refer to my guide there).
2. If you have completed every other achievement and are yet to complete this (less likely but maybe you accidentally left the radio OFF the ENTIRE time), download the MacroGamer software by searching for it. Use a macro to set the radio to turn on and off every 5 seconds (you will have to spend some time learning how to use it as it's a bit difficult to explain here). Once you have the macro set up, use it AFK for roughly 14 hours.
Remember you cant work toward any other achievement when doing this so if you want to, please refer back to the first option.
Good Luck