From the Super Mario Wiki
Elephants are enemies in Wario World. They are only found in Wonky Circus. They will try to attack Wario by charging up and ramming into him, and are invincible while attacking. Elephants are highly aggressive and resilient and require a Piledriver, Wild Swing-Ding, or Mega Toss to finish them off. The Elephant's rider, however, is extremely weak, and requires only the weakest of attacks to be defeated. Wario can defeat both the Elephant and the Elephant's rider for Coins, in a similar manner to Cobras. Wario does not sweat when lifting an Elephant above his head.