Hera Clip
From ALttP Speedrunning Wiki
This clip allows 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 and jump south through the screen transition, Link can wrap up to the top of the screen (although the camera will still be positioned at the bottom of the mountain). This is what allows us to get to Hera from the bottom of Death Mountain.
Spindash easy way
There is a very easy way with the Spindash trick. Do a spindash and clip with 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.