By Hookshot Jumping from either of the brick walls in the mirror room you can go OOB and land in the loading zone. Skips Lullaby use, Slug room & Mirror puzzle.
Use the hoverboots from the top of statue on the right to grab the top of the block and cross over it. Video also shows setup.
It is possible to reach the Mirror Shield chest from the outside of the Spirit Temple without ever having entered it. This is done by first performing a high Hookshot Jump off of one of the flagpoles onto the heart piece platform. Once on top you can either do a precise hover HESS or a hoverboost onto a seam on the statue. From the seam you can backflip onto a higher place then run up to the arm of statue and hop onto it.
You can use entrance point glitch and void in the room to go out of bounds, getting the skulltula from behind.