Meaning
To hold on for dear life / To seize an opportunity
Example
Precisamos agarrar essa chance com unhas e dentes!
We need to seize this chance with everything we've got!
Origin
The expression agarrar com unhas e dentes ("to grab with nails and teeth") evokes the image of clinging to something so fiercely that you defend it with every part of your body, refusing to let go.
Source: Priberam.
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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 workBater as botasTo kick the bucket / To die