From the Super Mario Wiki
Bullies are Bob-omb-like creatures that lived in Lethal Lava Land during the events of Super Mario 64 and Super Mario 64 DS. Their name and design are based on the word 'bully', referring to their aggressive behavior, and a 'bull', referring to their horns and charging attack pattern. A Bully resembles a black sphere with green feet, angry eyes and two bright yellow bull horns.
Super Mario 64
In Super Mario 64, Bullies usually reside on platforms, occasionally in groups. To attack, Bullies charge themselves into their enemies in order to push them over ledges, knocking their enemies into lava or bottomless pits. The only way for Mario to beat a Bully is to push it into the lava. After being melted, a Coin will be tossed up to the platform thay the creature was pushed off from. They are supposedly minions of the colossal Big Bully. They also appear in Bowser in the Fire Sea, the second Bowser boss level.
Super Mario 64 DS
In Super Mario 64 DS, Bullies appear with the same role and behavior as before. In the remake, Yoshi, if used, must stomp them to push them back or use a cap, as his tongue has no effect on the Bullies. A new Chill Bully king by the name of Chief Chilly appears as a new boss in the remake who holds Wario captive and must first be fought by Luigi.
Super Mario 3D World
Bullies reappear in Super Mario 3D World. However, their appearance has changed: they are now made of a blue shiny metal, their horns are golden and are bent forward with dark stripes at the base. Also, they have rims just above their feet and red eyes. They no longer grunt, and make a metal sound when jumped on. They once again charge at the player, and can be knocked back using projectiles like fireballs. Bullies will pause and teeter when pushed to the edge of a platform, giving the player time to land the final hit. If they are not knocked off, they will regain their balance and continue charging at the player.
Bullies cannot be defeated by any means other than knocking off platforms (excepting the Lucky Cat Statue), as even the Mega Mushroom will only knock them back when touched. However, this is also the only way they can defeat players, as they are one of the few enemies who do not deal damage when the player touches them.
Names in Other Languages