Super Jumps (SJs) allow the player to essentially jump off of walls. They are only possible with the Roc's Feather, and the types of walls Link is able to SJ off of are most commonly found in dungeons and caves.
SJs exist because of an oversight in the code regarding how Link hops down a ledge:
The introduction of the third check fully patched Extended Ledge Jumping in v1.1 and v1.2 of LADX. ((see Version Differences). It is unknown if the developers also knew about SJing during the update process, however the extra logic had a drastic effect on how far SJs can span.
SJing is most commonly done with a weapon. The following steps describe the execution process of a successful clipped SJ:
If done correctly, Link should jump off of the wall shortly after using any of the weapons described above.
Most of the time clipped SJs will fail because the user is accidentally pressing another direction during the transition from the direction towards the ledge to the opposing direction on the D-pad. Make sure to not slide your thumb to the opposing direction, but rather remove your thumb from the D-pad entirely, then start holding the opposing direction.
The directions above are still applicable to versions of LADX where Extended Ledge Jumping are patched, but steps three and four must be done much later into the jump (when Link is about to hit the ground)
Shortly after performing the last step, Link should jump off of the wall, finally allowing you to let go of your sword button.
Wall clipping is not needed for this method, however the trick will be made much less consistent, requiring many retries to work. It can be made consistent only when Link's X and Y sub-pixel values are set to 0 (which is always done after Link warps somewhere), but the issue in this case is that Link will only be able to do consistent unclipped SJs downwards or leftwards. Fortunately there is a consistent unclipped SJ method, mentioned below.
Pegasus Boots Super Jumps (PBSJs) allow Link to SJ off of any wall regardless of his sub-pixel coordinates.
Shortly after the unpause, Link should quickly jump off of the wall. Pausing can be done before jumping - this just means you'll have to buffer the jump and mash the weapon inputs while holding the direction.
PBSJs typically fail because of bonking. If this is happening to you, keep in mind that Link starts dashing after his fourth "step" sound. Use that as an audio cue for jumping and/or pausing. Also, try getting farther away from the wall if you can help it.
SJs without weapons (commonly referred to as naked SJs) are most useful when in situations where equipping a weapon is a waste of time. However, they are the most difficult due to the awkward inputs and timing involved.
If you held down for long enough, didn't hit any accidental inputs or accidentally lose your wall clip when trying to face away from the wall, then you should jump off of the wall. The second step can be replaced by using a charged sword slash to allign Link's direction without having to risk losing the wall clip (as seen in the Goomba Surf trick)