After the first part of the Oceanhorn battle concludes, wait for the change of venue, then pause and return to the title screen. This will return you to the boss room when opening the in-game save file. You are now free to leave the room via the southwest exit and travel the ocean to refill your heart meter and restock on store items.

When fighting the second battle, when the apparition appears simply hold down the shield button the entire time you strike to avoid unnecessary combat.

--NOTE: If after game you find your completion percentage to not be 100% double check that you completely explored Arcadia Ruins.--