This achievement requires you to play 100 in-game days (not real life days), that's going to take you about 33 hours. Sleeping will not speed up the process.

The best and easiest way of getting this achievement is to put your Xbox on "Never Turn Off" (required) in the settings and Appear Offline (optional).

After that you want to start a Survival game (Creative won't work) and put it on Peaceful Mode.

Then just leave your xbox and come back in 33 hours or so. Then the achievement will be yours.

If you need any help feel free to PM me.