High Jump
By holding UP and JUMP and pressing GRAB+DASH on the same frame while stood still or walking on the ground, Peppino will jump higher than usual in a Long Jump state. This enables you to reach and wall-run up ledges you were not expected to, or cancel the dash into other actions like Grab to alter Peppino's trajectory further. Most people do not hold JUMP prior to pressing GRAB+DASH but instead press JUMP on the same frame as those two inputs. However, jump can also be held a frame after those two inputs.
When performed, Peppino shoots up with the vertical velocity of a grounded uppercut (13.5 speed). High Jumps can also be performed during a Fast Walk to preserve horizontal momentum when High Jumping. However, the horizontal momentum of fast walking will only be preserved when High Jumping to the right and not to the left.
While pressing two buttons in one frame with an additional two frame input can be tricky, a Taunt or Uppercut can be used to buffer the trick, making it more consistent. High jumps can also be pause buffered by pausing the game, holding DASH, holding JUMP which unpauses the game, and pressing GRAB a frame after.
Wall High Jumps can be performed by doing normal High Jump inputs on the first frame when climbing a wall when jumping into a wall during a Mach Run state. Wall High Jumps have weird horizontal speed properties as Peppino's horizontal speed will decrease at a rate of -0.10 per frame and will be very slow when landing on a wall or floor.
High Jumps can also be performed in midair under certain circumstances, such as: Splatting on a wall. Throwing an enemy. Parrying an enemy.
Noise Variation
Noise can use the same high jump technique, with the exception that the up button being used for the high jump must not have superjump bound to it (including that the directional superjump must not be enabled), otherwise Noise will just superjump instead.
Noise's high jump has a much higher vertical speed than Peppino.