There are 9 shrines in the Dueling Peaks region.
There is nothing special in this shrine. Simply glide your way to the end.
The first use of Cryonis in this shrine can be skipped with a Shield Jump. The ball puzzle at the end of the shrine can be completed without Cryonis by first using Stasis on the ball as soon as it spawns, then shooting a Bomb Arrow such that the ball is shot up the slope and lands in the hole.
There are ways to get up to the ledge encompassing this shrine, making it possible run and glide straight to the ending.
This is the fastest method. By placing a cryonis block and shield jumping off of it right as it's rising, you can do a high shield jump and then detonate a bomb to get extra distance and height.
Place a Cryonis ice block underneath, near the end of the floating platform. Place a second block just in front of that and the platform should rise up, allowing you to climb up it and jump to the top.
Place a Cryonis block underneath the center of the floating platform then jump on top. Turn around, Shield Jump to the blue lamp, then jump to the top of the protruding ledge. Face the ledge behind you and Shield Jump up to it.
Stand on top of the floating platform and drop at least two Octo Balloons. Wait for the platform to rise then jump to the top.
This next video demonstrates the three previous methods.
It is also possible to do the second method without using the wooden platform at all, but it is much harder.
This is a Blessing Shrine.
This shrine has three ball puzzles, all of which can be skipped. The first gap can be jumped by Shield Jumping into a glide or by Bomb Jumping, and the subsequent gaps through Bomb Jumps also. At the third puzzle, Stasis can be used on the depressed button to tilt the platform, instead of using a barrel.
The ball puzzle in this shrine can be skipped by climbing high and gliding to the ending. Ride the platform up and jump (Shield Jump for extra height) just as it reaches the top, putting you on a higher ledge. Alternatively, use a Shield High Jump to reach it. From here, Shield Jump to the indent behind you. Now either glide down and Damage Boost your way over to the ending, or more easily Shield Jump (unequip shield) onto the big lamp, climb up and glide from there.
This is not faster than beating the puzzle normally.
The strategies for Shee Venath are the same as for Shee Vaneer, with the only differences being that the shrines are flipped.
This is the combat teaching shrine.
It is possible to to skip moving the various gyro platforms in this shrine. For the first, Shield Jump from the lamp then onto the block, or simply glide from the lamp past the block straight to the other side. For the second, either Shield Jump onto the railing, or glide onto the stairs to the right. Jump to the furthest stairs and from there Shield Jump to the ledge. The final terminal can be completed with only one rotation, and skipping the Small Key locking the door to the ending.
Make it across the third gyro structure. On either of the ledges, perform a Bomb High Jump followed by a Turnaround Bomb Boost. You'll make it over the fence.
Alternatively, position the gyro platform carefully so you can then jump from it to a big lamp, and from there bomb boost to the end.
Position the gyro structure as shown in the image below. Jump on the lamp, glide to the structure and stand on the torches to collect to open the chest. Glide to the locked door and open.