The Daily Challenge is a set of 3 different Minesweeper modes, one in easy, one in medium, and one in hard, each day. The game is still Minesweeper but games vary from puzzles where you have to flag everything you can flag on a chosen board (Flags), get a certain number of taps without blowing yourself up (Taps), detonate a certain number of mines in a certain number of moves (Detonation), or the best, find the 8 on the board (Treasure Hunt).
To unlock this achievement, just play 5 days in a row. You are not required to win, but for the sake of this achievement, it may be safer. Reports seem to be unanimous that the achievement will unlock during the SECOND challenge played on the fifth day.
If you do not want to wait, you are able to both go back and play 5 days in a row, or even go forward. In order to do this, however, you MUST first set your computer's clock to match the challenges of the day you're playing. If you play a challenge on a day that does not match it on the calendar, it will not count.
(Credit to planting42
for info about changing the system clock.)