A Daily Challenge badge is rewarded at the end of each month,
so this one will take you a full year to complete.
EDIT: If you have premium, you can go back to September 2020 without touching your phone settings, making the achievement available as of August 2021.
If you don't want to spend money on premium, then you can go into your phone's settings and set the date to 31st of Dec, 2020, and you will have access to November and December, saving 2 months of your time!
More on this in the "Note on Date & Time + Warning:" spoiler.
To earn them you need to do Daily Challenges and earn points from them, luckily, each badge includes the ones below it, so if you earn Gold, you will also get Silver and Bronze.
- Bronze ≈ 30 puzzles, or about six days of puzzles.
- Silver ≈ 60 puzzles, or about twelve days of puzzles.
- Gold ≈ 90 puzzles, or about eighteen days of puzzles.
- Diamond ≈ about 120 puzzles, twenty-four days of puzzles.
There's a total of 140-155 puzzles per month, so you've got some room if you find some too difficult.
Note for people reading in/after Dec 2021:
Note on Badges:
Note on Date & Time + Warning: