I finished Eric/Erik/Erica transformation, for some stupid reason I was using the walkthrough of v0.340~ instead of the latest v0.352.
But that is not why I'm posting. I was searching for this mythic "eric's quest" because people kept mentioning and I thought it was an actual quest, but there isn't. Anyway, I don't know how I actually unlocked but I do think it was having enough Fina friendship points to unlock the A Matter of Order quest and meeting the priestess at least 3 times during hunts with Eric.
I'm just making this post so anyone in the future searching for this "eric's quest" can use this as guidance.