Confirming Faye's solution.
This achievement is indeed earned by getting GREAT on every phrase in a song.
After grinding through the game for a long time (I had managed to unlock the Dog character), I finally found a song that was easy to get GREAT on all phrases.
It is a Korean children's song called "Butterfly". Unfortunately at the time of writing Korean script is not supported in solutions, so I have linked to a video of the song which shows the name in Korean. Note that the video lists the "artist" first, not the song name. In the song list in game, the "artist" is listed in brackets.
It only has 36 phrases, and they are very easy to get, so you should be able to pass it with ease even using a microphone and a fan (I have mine feeding game audio straight back into the game).
If you're still having trouble for some reason, you can use the video to learn the song.
Best of luck!