I'm curious, because when looking at soldiers from these time periods I can only think of soldiers trained to fight in large formations. I know "ancient times" is a large window but I mainly mean everything pre-medieval.
Celts (Gauls) had a tradition preceding battle where one or more warriors would break rank to challenge the bravest of the enemy to a duel.
In his book "The Celts", Gerhard Herm references Greek historian Diodorus. In Diodorus' writing on the Celts he is likely referring to Gauls in particular:
"Before [the battle] began, however, they indulged in a performance that was bound to confuse their enemies more than anything they had seen before. It started with one or more of them leaving the ranking and challenging the bravest of the enemy to a duel. As Diodorus recounts: 'At the same time they swing their weapons about to intimidate their foe; if anyone accepts the challenge, the Celtic warriors break into a wild singing, praising the deeds of their fathers and their own prowess, while insulting and belittling their opponents, to take the edge off them before the battle begins.' It was a ritualized psychological warfare, of a kind still employed in pub brawls in Alpine village-inns or Breton fishermen's taverns. But there was more to it. After this prelude, the Celts would begin their own moral preparation: 'Weird, discordant horns were sounded', swords were beaten rhythmically against shields, rage and war-lust were systematically whipped up. At last the first warrior broke ranks and stormed forward."
Apparently the early islamic armies had groups of specialised duelists to kill enemy officers and champions.