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Reduce the AP Cost of Unarmed Attacks in VATS.”
Beautiful Beatdown reduces the action point cost for unarmed attacks by 10%.
In order to get this perk, you first have to complete A Fistful of Hollars, which will unlock Destroy Something Not So Beautiful, which in turns rewards you with Beautiful Beatdown. The Old-Tyme Brawler challenge has the same requirements, but will only give you the achievement, not the perk.