Hera Clip
From ALttP Speedrunning Wiki
This clip allow you to enter hera without the use of the mirror, but it's more a time saver than a way to skip mirror.
When you clip at the bottom of death mountain, sometime you get teleported at the top of it. That what this trick use.
Spindash easy way
There is a very easy way with the Spindash trick. Do a spindash and clip with >v at the bottom of the right edge.
One you fall, press right, then up (to get out the border of hera tower), move down and try to enter Tower of Hera.
This image show you where Tower of Hera is exactly.