Hi Craig. In spanish there isn't a literal phrase to translate dog eat dog, the words translated are: perro come perro, but it doesn't mean anything in spanish, but if you want to know how to explain in spanish the meaning of dog eat dog you can say:
Dog eat dog es una frase que describe una situación en la que una persona está dispuesta a hacer cualquier cosa para tener éxito, aunque eso implique dañar a otras personas.