Credit to Cosminiion, who posted this as a comment in the primary solution. I wanted to write a concise guide for future use for other players THIS WILL WORK IN WIN 10
There is a clear way to do this and reliably unlock the achievement. You may be able to shed some steps off of this process, but i'm just sharing what worked reliably for myself. I didn't do this "legit" as I have far too busy of a schedule to even attempt such a thing. So I started this with zero progress towards the achievement.
Keep Task Manager and Windows Time Setting pages open, you'll be using them a lot.
1) Disable "Set Time Automatically" and reset your clock to the first of any given month at 12:00 PM (I used October 2018)
2) Open Minesweeper, and play an easy challenge from the first day. Allow all of the animations to play out. Don't skip any.
3) Open Task Manager. Once the coins finish collecting, wait between 5-10 seconds, and then close Minesweeper through the task manager.
4) Once "Microsoft Minesweeper" Disappears from the task list. Change your date to the following day. If you are doing this in one setting, you will not have to change the time at all (Thus why I set it to Noon) and you won't have to worry about the time of day disrupting your progress.
5) Open Minesweeper, and play the next Easy challenge on the 2nd of the month. Once again allowing all of the animations to play out, wait 10 seconds, and close minesweeper through the task manager. Go back to your settings, and move the date forward to the 3rd now.
6) Continue playing 1 daily challenge and moving the date forward in this manner all the way through the entire month.
7) Once you've completed 1 challenge for each day of the entire month. Close minesweeper like you have been doing through the task manager.
8) Now Reset your date to the LAST DAY OF THE PRIOR MONTH. In my case it was September 30th. Complete a single challenge on that day, and close minesweeper through the task manager.
9) Move your date back another day, to the 29th, and complete another challenge. Close minesweeper through the manager.
10) Now reset your date to the LAST day of the month you are attempting the achievement on (In my case, October 31st 2018).
11) Open Minesweeper and complete the challenge that you already completed.
12) Upon finishing the challenge (I actually failed on mine) the achievement will unlock.
-The prevailing theory seems to be that you need to complete the last day from the prior month in order to count a full month for some reason. So playing the 29th MAY be unnecessary. But you do you.
-Others have said you need to fail on the last day to unlock, I don't know if that's true. I meant to succeed in my last challenge, but out of sheer coincidence I failed. So I wasn't able to test that, but it unlocked. So you may want to fail it to be safe. Similarly, you might still unlock it by doing a different challenge rather than repeating the same one. Again, you do you.
-The whole thing will take between 60-90 minutes. I didn't even finish a single podcast episode.
-And as you noticed on my name, your time stamp will be distorted based on how you manipulated the calendar. So if you're a stickler for that sort of thing, be sure to attempt this on the last day of any given month so it's at least close to the correct date.
-Again, NOT my solution, but it seemed like it took me an hour just to collect everyone's theories and compile it into a successful (and single) attempt. I just want to make sure others can unlock this reliably!