Found a spot in Halls of Stone where you can Demon Leap or (I assume) Blink through the wall.
Head up into this corner, face this way, and Demon Leap/Blink. If you face to your right, you'll likely just soar off into space which might work, but make sure you have a slowfall ready right away. Otherwise move forward a bit inside the wall.
Pop a slowfall, and jump off into the void!
In Halls of Lightning, in the first area find the spot where a rubble pile butts up against the wall of the walkway.
Nestle yourself in between the rubble and the wall, pop your Darkmoon Tiger, mount up.
Dismount, and drop to the floor below! You don't even need a slowfall. From there, head out any direction through the walls to explore outside.