to work like a horse; to knuckle down; to have it out; to have a shouting match
A fixed idiom meaning to work hard, strive, or fight tenaciously for something — often for a modest or thankless goal: se batió el cobre para sacar adelante el negocio. It comes from coppersmiths' workshops, where hammering (batir) a copper sheet into shape took loud, tireless, repeated blows — a folk image for stubborn effort documented as far back as Covarrubias's 1611 Tesoro de la lengua castellana.
Despite containing cobre (copper), this has nothing to do with metal in modern use — it's a fixed idiom for hard effort/struggle, not a literal or industrial verb.
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"batirse el cobre" means "to work like a horse; to knuckle down; to have it out; to have a shouting match".