You will need to play the game for 100 ingame days, which translate to 33 1/3 hours. (1 ingame day lasts 20 minutes). You do need to have a controller charged while going for this, as the game only progresses (and counts progress) when you are not in the start menu. In case you don't want to play the entire 33 hours, start a game on peaceful (so no mobs can kill you) and be sure that you can not accidentally die of any other reason (drowning, falling, lava, etc.) Then plug in your controller, turn your tv off and let the game idle.
You can track your progress both ingame and in the achievements tab.
-Mouse and keyboard works as well.
- joining someone else's game doesnt always seem to count.
Update based on comments:
- Turning off controller works
- Sleeping at night works as well and it tracks.