I encountered the same problem that Davehx was having. I'd recommend doing it in a February as that's the shortest month of the year.

When the final date's challenge is complete, the achievement will unlock. Work all the way up to the final date of that month, in order. Complete a challenge, close the game, and set the date to the 2nd. If you want to go for it the fastest way, set your computer calendar back to the 1st of a month you have not completed any challenges in. This method can be used on any day of the month, so if you start the game on the last day of the month, you could unlock it the same day. Repeat this until you get to the day that you are on and then finish it normally for the rest of the month. Open the game back up and complete another puzzle for that day. After that you need to close the game and then set the date for the second of the month. If you're starting this after the first of the month, then you can set your date back to the first and complete one puzzle. You will need to do this each day of the month.

Simply come back each day of a month, starting on the first, and complete at least one puzzle each day.

Microsoft mahjong extra 25 achievements