Haxorus can have the following abilities:
Rivalry: Attack & Special Attack is increased by 25% if the foe is of the same gender; Attack & Special Attack is decreased by 25% if the foe is of the opposite gender.
Mold breaker: The Pokémon's moves are not affected by foe’s abilities during battle
hidden ability: Unerve: The opponent Pokémon will never use their held Berry while the Pokémon is in battle
Hope it helps :)