Taiko no Tatsujin: The Drum Master!

This achievement is for earning 50,000 coins. It does not count the 500 coins you start with, so if you're holding all your coins for the "Saving Money is My Hobby!" achievement, it won't pop until you hit 50,500.

Easiest way to obtain coins that requires no skill:
1) Select the song "Hopes and Dreams" (in the Game Music category)
2) Press and change the following settings:
- Special: Perfect
3) Select the Extreme difficulty

It will fail immediately, giving you 10 coins. Depending on how fast your Xbox loads the song, and how present you are to hit the button, you can get get somewhere between 2200-2500 coins per hour.
Credit to TA members weffalump and james bogart for this solution

Other ways to obtain coins:
Ranked matches
Each Ranked win is worth 200 coins. A few times per day they run a Double Coin bonus for two hours, so you can win up to 400 coins per win. You still get 40 coins if you lose. Also, you get an additional 100 coins for every 10 ranked wins you get.

Obtaining silver/gold crowns on every song
The first time you obtain a silver/gold/rainbow crown on a song, you get bonus coins. You can earn these crowns for each difficulty, so if you're decent enough, you can get a silver/gold on Easy and Normal difficulties. If you are going for all of the achievements, you need to complete each song anyway.

Completing the three daily bonus songs
Each bonus song will give you 100 coins. You can leave the "Perfect" mode on if you'd like, allowing you to finish all three songs in about a minute.