When you have the correct necklace equipped you will be able to fight the 'true' final boss at the end of the Firmament level. To achieve this you must first collect the 7 hidden jewels that are scattered across each stage and speak to Joule who will give you the Handmade Necklace as a reward. If you now beat the Firmament level with the Handmade necklace equipped it will turn into the Broken Necklace which you must wear when beating the Firmament level yet again.