The white orb is found in anti-souls mistery lab. In the room with the flame zombies and frost zombies there's a statue. You need to destroy the statue using the flame whip and the frost whip in order to proceed to the chamber behind it. In that chamber you will find the white orb. The black orb is obtained after you beat the forgotten one (optional boss). Unfortunately i don't even know how to enter the room were it's located. The door to the forgotten one is sealed by an enormous power but i don't know how to unseal it.
Well the jumps are tricky there since I believe you need to do a series of double jumps plus whipping the railings to pull yourself up to the ice elemental boss area.
As for the black orb, you need to defeat the Forgotten One for that. And to access his room, you need the Unlock Jewel in the Pagoda of the Misty Moon area. The item is tricky to find because it's on a platform in of those rooms covered in almost total darkness. You basically have to blind jumps.