Bully Battery is a glitch that uses speed from knocking an out of bounds bully repeatedly to allow Mario to gain hyperspeed.
If a bully is out of bounds, Mario runs into the bully repeatedly in order to very slowly cause the bully to gain speed with each hit. After, we can transfer the built speed back to Mario to move at hyperspeed. However, Mario needs to either use water or a squish cancel to escape the knockback state. Otherwise, the built up speed is immediately lost. The glitch is used to access to beat the star Elevator Tour in the Volcano in 0xA-presses and is currently being used as part of a theory for a method to beat Bowser in the Fire Sea in 0xA-presses on N64.
Fast Bully Battery
When Mario gets hit by the bully, the bully speed is transferred to Mario after being multiplied by a conversion ratio of 3*73/53. This would put Mario in the knockback state and cap his speed, but with Squish Cancel, Mario can switch to the Squished state then switch into another state, bypassing the cap and keeping his speed.
If Mario now gives this speed back to the bully, it is multiplied by a conversion ratio of 53/73. Overall, this corresponds to the bully's speed being multiplied by 3. Thus, the Bully's speed increases exponentially, with a speed increase on the order of .
Slow Bully Battery
When the bully already has speed, Mario can give it even more speed by hitting the bully perpendicular to its velocity vector, giving the bully a new speed according to
Assuming Mario's speed is constant every hit, the bully's speed will equal by the nth hit. The speed is gained very slowly, making it potentially take upwards of months for useful speed to be obtained but it is much less restrictive than the other method.
Pole skip using hacked bullies: https://www.youtube.com/watch?v=14_srcwQ4Lw
LLL Elevator Tour in The Volcano using Bully Battery: https://www.youtube.com/watch?v=IrXqE6DDt0I