Hookshot Jump is a glitch which causes you to shoot up high into the air by canceling the hookshot animation as soon as the hookshot latches onto something. There are several methods to perform this glitch. It is important to note that the higher up you aim the hookshot, the higher you will go.
Latch onto something while on Epona (you need a blank B button to use hookshot on Epona), then fly to the place you shot and you will get a hookshot jump, depending on how high you aimed.
To do this method, simply die at the same time your hookshot latches onto something. You can die with damage or heat/breath timers running out. Having a fairy will allow you to revive after the jump. Also, using this method while underwater (with iron boots on) will cause you to shoot much higher in the air.
This method is rarer but can still be done in several places, such as Dodongo's Cavern main room and the Darunia room in Fire Temple. Use the hookshot to latch onto something immediately before a cutscene starts and you will get a hookshot jump.
This method is more complicated. You must kill a gold skulltula, then jump into the token and use a cutscene item (such as a trade item, ocarina, or a bottle item) right before you touch the token. This will delay the token text until the camera faces the location the token was at. Next, use the hookshot so the text get brought up right as the hookshot hits a target. When you cancel the text, you will shoot up very high in the air.
First, get the First Person Item Lock. Have the hookshot in your hand, then while holding z, roll and bonk into a wall, then mash the hookshot. If done correctly, the camera will be zoomed in on link's back and he will start to pull out the hookshot every few seconds. Starting on the 3rd time he does this, quickly use and release the hookshot on the first frame he holds the hookshot up all the way to get a hookshot jump. Make sure you aren't touching the control stick during the hookshot input, as that will make it not work. If you are underwater or have the gravity glitch active while you perform this hookshot jump, you will go much higher.