There are two "canon" ends, and they're the ones where Mezz leaves the island...under his own power. The one in the cage doesn't count, as the story doesn't "continue" from there. Either one of the two canon ends will get you the DataCrystal file.
My brain is a little fried at the moment, but check out my "Scene Guide" devlog here, it describes how to get each of the endings. If I remember right it's lose to the boss with less than 3 mob defeats, loop once, lose again, and give in rather than struggling in the kneeling scene.
