[original] : Il a beau avoir été élevé dans une société martiale, il ne recule devant aucune perfidie pour arriver à ses fins.
Normally, in the « avoir beau X, Y » expression, X and Y represent opposite ends of the spectrum, thereby making Y surprising. So it would make more sense if Y showed a stark contrast to X:
Il a beau avoir été élevé dans une société martiale, il excelle dans beaucoup de domaines.
Despite X [= he has grown up in a society that has known nothing but war],
he is surprisingly Y [= he excels in many fields].
In the original sentence, however, the relation between X and Y seems more like « X, alors Y », which deviates from the usual way this expression is used:
Because X [= he has grown up in a war-ravaged society],
naturally, he is Y [= he will stoop to anything to achieve his ends.].
Or perhaps, at least in the eyes of the speaker, X and Y somehow contrast strikingly with one another?