What is a hyperjump?

See here for some gifs.

How to:

To perform it, start by holding the analog stick diagonally forward and down to run. Next, hit the dodge button. This will start a dodge slide, which you can immediately cancel by jumping. Keep holding forward and you’ll retain your speed boost for a distance. It’s important to hold the stick diagonally forward and down at the start. Holding just forward, you’ll enter a regular dodge rather than a slide. You can still jump out of a regular dodge of course, but dodge slides are faster and give you more distance.

Note:

Keep in mind that Super Jumps are a form of dodge cancelling - this means that your dodge cooldown starts from the moment you jump. All dodge cancels leave you vulnerable, unable to catch arrows for a short time, gaining you mobility in return.

Like @Seiyria mentioned, a SuperJump is a way to jump far and fast using the following combination:

• Crouch (diagonal forward)
• Dodge
• Jump, which will cancel the dodge

It allows you to do a slightly better jump, retaining the speed of the dodge.

For HyperJump, which is different, you have to know about Tap Canceling.

Tap canceling is when you Dodge while already Dodge, which actually cancel the first dodge while keeping original speed. It has multiple uses, but if used but the SuperJump technique, can lead to HyperJump, so the order is:

• Crouch (diagonal forward)
• Dodge
• Dodge again (the sooner the better, but not on the same frame)
• Jump

And you'll HyperJump! Do note that in SuperJump and HyperJump, you can still fire arrow (which is a way to surprise your enemy) but since you just canceled your dodge, you cannot catch arrows or dash on a monster (solo mode) to avoid being hit.

It requires a lot of practice to learn how to use it properly without killing yourself, so be careful to not abuse it.

http://towerfall.wikidot.com/how-to-play will have some additional information.