This achievement must be obtained on 1/21, which means you have two ways to go about it. You can wait until January 21st, or you can re-set the time on your Xbox One. To change the date, unhook your One from the internet then do a hard re-set (hold the power button down for ten seconds). You should now be able to go into Settings and change the date. I don't know that the year matters, but I chose 1/21/2017.
You will have a new character available who has some pretty nice skills, so you might not want to leave this for last like I did. If you keep him alive for three floors and/or finish the game with him, he will become permanently unlocked like your others. I don't think it matters which pod you use, but I stuck with the Escape Pod on Too Easy.
One thing to be aware of - the description of this achievement is a bit deceiving. You don't have to just "play" on 1/21; you must win a game, so instead of the two minutes I was expecting, it was closer to two hours. Also, the achievement didn't fire when I finished the game. It was not until I went back online, turned my Xbox off and on, then opened the game again that I received the achievement, so it's a bit buggy.