Three Fourths Home: Extended Edition

Once you have completed the main game, the radio will become available in Extras. UPDATE: according to iMaginaryy the radio is available from the start of the game. Additionally the radio can be started, and then you can look at the other extras in the game (although they not available until you complete the main story and epilogue).

You must listen to every song in the game all the way through, using the radio in the Extras. Listening to songs on the radio in your car as you play the story does not count. The simplest way to do this is to start the first track and then walk away for about 50-55 minutes. The game will move through the tracks by itself, you do not need to skip tracks (actually skipping tracks will probably void that song from being counted).

After all the tracks have played and it cycles back to the first track again, the achievement will unlock.

Here's the full track list, thanks DivxKiller:

title (from [out])
dark, loud (from [out])
the hallway (from [out])
credits (from [out])
sea of bodies (from [out])
soundcheck (from [out])
decay, collapse (from [out])
crowded (from [out])
hobbled (from [out])
all over again (from letters to babylon)
and the wind will lift away our rot
idling in the rubble

Very easy but takes approx 55 minutes.

Just go to "radio", in "more" from the main menu.
Hit play, and it will auto play the next song.
You can just go AFK and leave it play.

I had a 55 minute timer on reminding me to come back to the game and it had just restarted the first song, so it's about 54 minutes.

You can do this without having touched any of the rest of the game.

( P.S: First song is "title (from [out])" and the last song is "idling in the rubble". Just if you're wondering where you might be in the list when you come back from setting a timer.)