Firstly, they dun need to.
Dexterity, naturally sharp claws/teeth, powerful bite, venom, stingers, acid, electrical shock etc serves them well enough to hunt other species. Learning martial arts is mainly for humans to fight against other humans.
I put 1 MMA fighter in a cage with a tiger. Which side you want to bet on winning?
Secondly, humans have trained animals to fight humans before. Guard dogs being most common in modern times, but in the past, there were war dogs, war elephants, predatory birds etc. Since their anatomy is different from humans, have to teach them to use attacks that is different from humans, tie sharp blades to their tusks etc instead of giving them swords to wield etc.
End serious mode. Now I present the obligatory martial art fighting cow: