Sie hat sich recht gut geschlagen.

English Translation

She did pretty well.

question: does this have a fighting connotation?

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No, at least not in the sense of a physical fight.
“She put up quite a good fight”
is a better translation.
In English that also can be a “fight” for rights, for recognition, even for a good grade in an oral exam, in sports, in a court of law, whatever.