Taiko no Tatsujin: The Drum Master!

This isn't like the other coin achievements where you just need to earn a total amount. Nah, this one wants you to be holding 87,600 coins at one time.

Best way to grind coins in my opinion is just enable the Perfect option (pick a song, open the options menu, and scroll down to Special, you'll find Perfect in there. Make sure you hit the button/Enter key to confirm), load up any song, wait until you fail, and repeat.

You can use a turbo controller (or if you're on PC an auto clicker can work too) to grind this out if you wish and I seriously recommend you do because trust me, this is not a grind you're going to want to actually sit through. You're only going to net about 3,000 coins an hour so expect this to take a while.

To unlock more coins for purchases or grinding towards the money achievements, you can play Ranked matches during Double Coin event hours. These events appear to occur at the same time daily according to Tis Shell, thank you for your comment.
During these events you earn about 400 for wins, 40 for losses. (But be aware there are a lot of smurf/cheater accounts so you aren't guaranteed to win a fair amount) Or you could grind out the song list on Easy and try your best to get a Gold Crown, this will get you the "First Gold Crown" bonus providing you get a Full Combo, you get these by not getting a single "Bad". "OK"s & "Good"s are fine. This will earn you 290 coins, the higher the difficulty the more coins you earn alongside Full Combo bonuses. But once you have a First Gold Crown on one difficulty for example, you can't replay the same difficulty on the same song and achieve the "First Gold Crown" Bonus. If you were to repeat the same difficulty on the same song, you will just get a bonus for Full Combo's which is about 60 coins.

You could play songs in Taiko mode, find one that has a fast intro note, (Hopes & Dreams in the Game Music category is a good one, thank you PhoenixWartooth for your contribution). Then before you select to play this song, press start and go to special and find "Perfect" if you confirm this along with 4.0 speed then if you miss the first note, the song will instantly end, putting you into the results screen, you will get an instant fail, this will earn you 10 coins regardless. This'll take about 20 seconds including loading times, this is also a good quick way to unlock the "Play Taiko Mode (MANY) Times" achievements.
Daily bonuses are on three songs each day and each of these will earn you 100 coins, these daily songs are distinguished by multicoloured stars on the side of the song.
Edit save or spend at your own discretion, I would probably not spend any coins until you breach the point of 87,600 coins and unlock this achievement, for the sake of possibly losing a lot of time on this achievement.

Input: Rather than down voting I would prefer for you to comment so i could adjust my solution to your benefit and further help others gain this achievement.

Good luck hunting, will edit if needed.

This solution is for PC

The fastest way to grind coins is to set the game on "perfect mode" and play the daily bonus songs.
You got 10 coins for the failure + 100 coins for the bonus. There is 3 bonus songs per day BUT, you can change the date on your computer to reset the daily songs.

I used to play the first two songs and during the third song, change the date. After the results screen, i got 3 new bonus songs, play the first two, change the date during the third... repeat.

With this method, i was able to gain 660 coins in less than 2 minutes. Approximatevly +19 000 coins per hour.

this is not the most convenient, but by far, the fastest. Plus : it will boost every other achievements