In this anime trailer the protagonist say this sentence:
I can't figure out the meaning... Is maybe something like "Fight like a man!" or "Don't play rough!"?
PS: here the context scene.
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"Fight like a man!" is more or less exactly what it means in this context.
More generally, it could mean something to the effect of "fight/play fair and square" or "fight/play without resorting to cowardly/underhanded means" etc. Here, the speaker seems to refer to the fact that the sitting guy is making the other two fight in his stead.
To break it down a bit more:
勝負する means "to fight", "to compete", "to play (competitively)" etc.
～てみやがれ！ (from ～てみろ) would literally mean "try to (x)!" or "how about you (x)!". In some contexts you would translate this, e.g.「この一撃に耐えてみやがれ」~ "(Go ahead,) try to withstand this attack." In this context, you could translate it as "Try fighting like a man!" or "How about fighting like a man!". Still, this sounds noticeably more literal (and clunky) in English.