Fez: Does anyone know how to unlock the second gamerpic on Xbox 360?

I'm asking here as well in the off chance someone remembers how to unlock it. I've combed the internet and there's no info on how to do it. I'm talking about the blue Gomez one, not the white Polytron one.

So anyways, back in the day I completed Fez on the 360 all the way to 209.4% and had all the achievements but yesterday I was fooling around with 360 backwards compatibility and long story short, I changed my gamer picture and seem to have lost the Fez one forever. I dusted off my old 360, made a second account and started playing again but I still haven't unlocked it. Is it tied to a specific achievement? Do I have to 209% it again? Please, if someone could tell me, that would be awesome.

Btw, I unlocked Get a Cube, Achievement unlocked and Equal and opposite, so if it's tied to an achievement, it's definitely not one of those.