My best advice for this achievement, and those for the bronze and silver medals, is to go for all the Match Attack and Score Attack challenges first. It seems like there is always one of these for each day of the month, and they are by far the quickest challenge, generally always less than a minute to complete, and I have yet to fail one even when they claim to be Hard or Expert.
Annoying as it is I would also recommend paying for a month of premium as the bonus coins will save you some serious time (doubles the coin reward for each challenge) and then manually change your phone/pc date back to the prior month, then the month before that, etc. to gather all the medals quickly (unless you want to spread it throughout the year!).
On average, if I do the "daily" Match/Score Attack challenge for each day of the month I can get the gold medal with those 30/31 challenges + 2 fully completed days with the bonus granted as a result of that.
As you will need a couple of complete days to get the Gold Medal, alongside the Match/Score Attack challenges, I recommend looking out for days where the Match/Score challenge is rated 4 stars. If the other two challenges for that day are Golden Tiles and Lightning Tiles then do both of those as well. These two challenge types are generally quicker than Classic (where you have to clear the whole board), and if the Match/Score challenge is 4 star difficulty, these should generally both be 1 star difficulty only, so this should be the easiest route to getting a daily bonus!
One thing to note, I'm playing this on a Lumia 950 XL and was consistently getting the game freeze up when I clicked "Collect Reward" after each challenge. Not sure if it's just me, or this is a general issue for everyone, but the way I found to avoid it was to wait for the little fireworks to go off after completing a challenge, then wait another ~10 seconds after that before tapping Collect Reward. The game then loaded back to the challenge selection screen fine, saving me having to reboot the app completely, and avoiding the pot luck of whether it would decide to give me the reward or not.