Until the last century it was somewhat common in Spain to pit a bull against another animals, usually lions, in a fight to the death.

What usually happened was that the animals would just ignore each other for the duration of the fight or the bull would kill the opponent, sometimes quite fast. IIRC in Zaragoza a bull killed a lion and a tiger so fast the police had to intervene because the spectators wanted the money back.

No English sources, but here there is a newspaper page with some interesting fights and results. And here you have the chronicle, including posters and photos of a bull vs an elephant.