Wall jumping can be performed by hitting the jump button while immediately next to (but moving away from) a wall, giving the player a second jump allowing for much greater height.
Wall jumping can only be performed while the player's charges are full, and only once between landing on enemies, doodads or the ground. This is because whether a wall jump can be performed is dependent on the player character's current sprite. If the sprite is rolling in the direction of the wall, they are able to wall jump.
If the player character jumps off the ground, an enemy or a doodad while holding a direction button their sprite will be rolling, allowing them to perform a wall jump.
Shooting, taking damage, jumping without holding a directional button or performing a wall jump will result in the player having a normal jumping sprite, which will not let the player perform a wall jump.