Most people don't realize it, but y'know in the Kilika temple where there's one of those flashy things in the ground that resets the location of the Pedestal? Well, push the pedestal on top of that. It shows a new Kilika sphere that you place in the exit of the temple. Take the Destruction sphere you found in that place you opened up with a glyph sphere, and place it where you just removed that Kilika sphere. That should open up the secret chest.

I hope that was clear enough to help.