After the boss attacks for a few moments, it put out a fleshy appendage. Slashing it with the Celestial Brush caused some hooks on the boss' top to come into view. Using the Brush, you can then attach them to flowers in the level which act as pulleys - pulling the boss' carapace open and allowing you to get close and smack the hell out of its unprotected eyeballs... which, for some reason, are arranged in a ring inside. We don't argue with malevolent spider goddesses about physiology, though; we just kick their asses.
Once we the boss was almost dead, it decided to up the onslaught by firing huge projectiles and trying to escape to the safety of the ceiling by climbing its thread - but a stroke of the Celestial Brush took care of both of those. In moments, it was slain.
