Meaning
To sort things out on one's own, to get oneself out of trouble (vulgar)
Example
Ninguém vai te salvar, se desenmerde!
Nobody's going to save you, figure it out!
Origin
Desenmerdar is a direct import from French se démerder, an informal verb coined around 1900 from dé- plus merde — literally "to get yourself out of the mess." Brazilian Portuguese borrowed the whole idea intact, vulgar register and all: the same sort-it-out-yourself-however-messy-it-gets attitude as the French original.
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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