Meaning
A battle of giants / Big league fight
Example
Eu não quero estar envolvido em briga de cachorro grande.
I don't want to be involved in a battle of giants.
Origin
The image is of a large dog's fight — one with fangs and real risk — compared to the skirmishes of small dogs. 'Briga de cachorro grande' became Brazilian slang in the 20th century for serious confrontations in business or politics.
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More idioms
Acertar na moscaTo guess correctly / To hit the nail on the headAmigo da onçaA fake/false friendAndar na linhaTo toe the line / To behave properlyArmar um barracoTo cause a public sceneRodar a baianaTo cause a public scene / To go ballisticArrumar sarna pra se coçarTo ask for troubleArrastar as asasTo hit on someone / To flirtAbrir o jogoTo come clean / To open upArregaçar as mangasTo roll up one's sleeves / To get to workAgarrar com unhas e dentesTo hold on for dear life / To seize an opportunity