The Mariachi Trophy
You sang a song in Karaoke Mode.
Karaoke Mode is intended to be a mode where you can just sing for fun. There is no countdown clock or score, just you and the lyrics on screen.
To earn this trophy, go to Main Menu > Karaoke. The (song length) setting can actually be on Short if you’d like, and you’ll still get the trophy, so do this to save time. For the setting, you can either choose Instrumental (music only) or Vocal (full song with vocals), it doesn’t matter. Simply pick a song you’d like to hear and let it play for the duration. Quitting the song early will not get you the trophy.
You don’t even need to have some sort of input into the microphone, whether it's the fan or your actual voice. I was able to get the trophy on an alternate account in total silence.
The trophy will unlock during the loading screen while you are returning to the main menu.