You will need to play for 100 in-game days. As far as I know, sleeping does not speed up the progress. You can track your progress, if you go to the ingame achievements tab. I would advise you to let your phone idle for a while.
One glitch which I'd like to add is that I unlocked this achievement while I was sleeping and my phone was in stand-by mode. (I could only change it to 30 minutes, before my phone would go into standby-by mode). This means that you could easily let your phone progress towards this achievement, while you are sleeping. I let it run for 2-3 nights, and each time it turned off after half an hour, but apparently I still made decent progress.
BulletLukey has made an awesome world for this. You can join our realm (as long as it still runs) or download the world yourself.
In this world, it takes roughly 3,5 hours to get the achievement!