You are given 3 daily challenges to finish each day. If you do not finish any of them then they will carry over to the next day. You can choose to replace one of the daily challenges each day if you do not want to do it. You will be stuck with the other 2 though. So if you get multiple you don't want to do then you will have to wait to replace on the next day.
The minimum amount of days you have to play is 17 to get this trophy. That is if you do all challenges except 1 over the 17 days, although obviously you can take as many days as it takes to get there.
Unsure how it works for other time zones, but for myself in GMT the challenges rotate at midnight. The caveat is they won't change until you restart the game. So if you have 1 challenge left for the day and you are still playing, as long as you don't close the game, you can get it finished and then on game restart you will get 3 new challenges. This also means if you have finished all 3 and are playing after the challenge rotate, you are best to restart the game to get the new challenges.