You'll see a Heart shrine right in front of you. It will be free once you activate the Blue Device and defeat the Goatlings. Afterwards you'll be stuck with some Agonofinis but they shouldn't be any trouble. Now charge up on the DT platform in the corner and fly up to the level above using Aerial Heart. Once you reach the level with Agonofinis, hop up onto the small platform with a single statue you'll receive Darts (don't forget the Blue Orb fragment beside it). Keep rising until you reach the room with the Blue Device which will activate another location above.
This boss is fairly easy. FIghting from afar would be rather tedious, so it is recommended you fight it straight on. Just make sure to avoid his swings and tosses of his ball and chain arms.
Get the piece of Arcana and the blue orb beside it. When you reach the top level that will end the mission.