Using the displacement that a bomb drop gives to Link in a frame (over 52 units in a frame), it is possible to clip through the barrier at a seam, due to float precision errors. There are 4 main position setups for this trick. They are listed below, ranked by speed.
For both sidehop methods, the following angle setup can be used instead of a manual lineup:
Here is the same method but showcasing an easier angle setup:
Angle cue explanation starts at around 9 minutes.
It is possible to unload the Hyrule Barrier. See the actor unloading page for more information.
After entering the Hyrule interior, roll over to the pillar on the right and perform a roll clip to enter the pillar. Now go down the stairs while staying inside the wall until you reach the bottom pillar. From here, put yourself next to where the floor ends and aim towards the void. Begin to crawl, and you should fall through the floor. Once you fall through, pull out the Deku Leaf and leaf to the loading zone.
After going down to the Master Sword chamber, head down the stairs. Pull out the wind waker and using either the bottom of the left or right banisters, preform dry storage. Now you will simply store the KoRL text once you hit the text trigger. Note that you must preform dry storage very quickly here for storing the text to save time.
After returning to the main floor, head down to the main level hallway on the right and go to the end to find a railing on your left. Climb up onto it, and then do a sidehop to your right as to get yourself into the proper position. Now turn around and pull out a bomb. Immediately after you press R to drop the bomb, hold up on the control stick just long enough so that Link grabs the ledge after getting pushed off (if you hold up on the control stick any longer Link will pull himself up onto the ledge and you will have to start over).
Right after Link grabs the ledge, tap right on the control stick to ledge clip into the wall. You will automatically fall down, and can now jump OoB and use leaf pumping to get to the castle exterior loading zone--bypassing the electric barrier altogether. Once you are outside the castle you can use either a savewarp or a death warp to return to the front of the castle and leave.
Note: If you were holding L to align yourself with the wall after turning around, do not continue to hold it as you set down the bomb, otherwise Link will not grab the ledge.
Although we do give this trick description based on the railing on the right side of the main room, you can also use the one on the left side of the room to clip OoB as well. However you cannot simply hold up on the control stick after dropping the bomb to grab the ledge and clip; Instead you must use the deku leaf to re-grab the ledge as is typical of most other ledge clips.
Note: You will not have to defeat the enemies when you visit hyrule for the second time. Instead, when you enter the castle for the second time the electric barrier will dispel and the music will play as if you just defeated the enemies.
After you have obtained all of the requirements to break the barrier leading to Ganon's Tower, head over to the back side of Hyrule Castle. Use a backflip or sidehop to get into the air and use the deku leaf to glide onto the bridge railing. Run over near to where the barrier is and jump into the void. You want hit the loading zone for the cutscene and then hit the zone for the void while it is fading out.
If you timed the jump successfully, you should respawn in front of where the barrier used to be, and no enemies will be loaded. However if hit the void first, you will respawn by the back entrance to the castle and the enemies will still be there. Either way though the barrier is destroyed and you've skipped the cutscene.
Although it is possible to get on the railing on the English version of the game, that method takes much more time and would be slower than breaking the barrier. It is due to the fact that the invisible walls around the railing are so much shorter on the Japanese version that this works for Japanese only.