"Zelda informs Mineru that she has come up with a plan to restore the Master Sword by performing an act that Mineru herself has said is expressly forbidden. It will consume Zelda's sense of self, but the princess insists that she will make this ultimate sacrifice. Mineru is gravely opposed, but promises to help to the best of her abilities."
When Princess Zelda traveled back in time, so did the Master Sword. Zelda explains to Mineru that the Demon King is vulnerable to the Master Sword and that it must be preserved. Over time the Master Sword can heal itself and grow stronger. In order to regain its strength, Princess Zelda makes the decision to undergo the dragonification. Mineru strongly opposes Zelda'a decision, but goes along with it. She mentions that even when she loses her body, she will help out in Spirit.
After seeing the memory, this wil begin the Trail of the Master Sword quest.