It will NOT take a full year to collect all 8 gold, 10 silver, and 12 bronze badges. Change your system clock to the last day of a previous month, and the full slate of challenges from that month will be available. This applies to ALL Microsoft Casual Games which provide daily challenges.
Depending on the particular assortment of challenge difficulties on a given day you choose to complete, any given day will yield in the neighborhood of 850-950 coins. This is based on most days containing 2 easy challenges (worth 100 a piece), 2 medium challenges (worth 150), and EITHER a hard (worth 200) OR an expert challenge (worth 300), and a 150 coin bonus for completing a day.
This means:
Bronze medals require 3 days of complete challenges
Silver medals require 7-8 completed days
Gold medals require 13-15 completed days
I personally found certain challenge types more difficult than others. While I could complete an expert Color Charge without a significant challenge, there were even medium Sprint Match challenges that I had trouble completing. So if a particular day contains an expert version of a challenge type you struggle with, avoid that day, as you will likely spend longer completing that one day's challenges than you might spend completing two entire other days with challenges better suited to your skills. Similarly, since expert puzzles are worth 300, they essentially provide a 50 coin bonus, as they skip 250 in the 100-150-200 pattern and go straight to 300. So if a day has an expert version of a challenge you excel at (again, for me this was Color Charge), make sure that's one of the days you complete. The difference for any given month is negligible, but expert challenges (assuming they're attainable for you) are more fun, and the little boost to your coin count will add up over your 12 months of challenges.
With all of this in mind, pick a given month, complete your 13-15 days of challenges within that month, and then change your system clock to the last day of the previous month (to give you access to all challenges within that month), get your 13-15 days of challenges, rinse and repeat 6 more times to get your 8 golds. Do the same thing for 7-8 days on an additional 2 months for your 9th and 10th silvers and bronzes, and finally complete 3 days of challenges in a final set of 2 months for your 11th and 12th bronzes. This will still be quite a grind, but if you're diligent enough, you could knock out these 3 achievements in a weekend rather than an entire year.