This will more than likely be the last achievement you get in the game. It requires you to play for 100 Minecraft days, which is equal to 33.3 hours of playtime. If you play Minecraft regularly, this should come naturally, as 33.3 hours is not too much time. But if you're just in it for the gamerscore, the best way to come about doing this is to set up an online game, with it set to 'invite only'. Once that's done, load up a survival world on peaceful and find a nice place to stand. It really doesn't matter where. From this point, all you have to do is hang out for however many hours you have left to do. I'd suggest doing this overnight, or while you're not at home. Once you're in the game, I'd suggest turning off your controller, to avoid wasting battery power. Since it's an online game, your controller being turned off will not stop the day-cycle so you can still work towards this achievement. After you've played for the required amount of time, the achievement will pop and you're good to go.
EDIT: As you may be able to tell from the comments, this achievement is extremely buggy. It works for some but not for others. If you can't get it to unlock, try the generic troubleshooting, such as clearing the cache, making a new world and starting over, disconnecting and reconnecting you account, etc. If all else fails, contact xbox support here:
http://support.xbox.com/en-US/xbox-360/games/minecraft-xbox-... by making a thread. If you see a thread already there for it, use that thread to post the issue. If they realize how many people are having the same problem, it'll have a better chance of getting noticed and forwarded to 4j Studios.