The Highflip is done by attempting to do a backflip while Link is in his crouching animation. You can get this animation by either placing items on the ground, getting out of water, or sidehopping.
There are multiple ways to perform a highflip.
Pick up an item that can be carried (such as a bomb or a rock), then drop the item with A. When Link begins to crouch down, perform a backflip as soon as possible. If done correctly, it will cause Link to start his backflip in mid-air, giving you extra height. The frame-window for this trick is small, so mashing A while dropping the item is recommended.
This trick requires a place where you can swim out of water without grabbing a ledge. Z-Target while you're moving toward land. Directly after Link exits the water either perform a jump/backflip to perform a highjump/highflip. It is also possible to do this while spinning toward land.
Note: The Water Dragon's Scale isn't required.
Similar to the drop method, backflipping immediately after sidehopping can also result in a Highflip.
The Highflip has only a few known uses. The Highflip does not give as much height as running up a wall, so it is only useful in places the where Link is unable to run up the wall or grab the ledge. The main known use for Highflip is to get the Blessed Idol early (non-NTSC 1.0 route).