This Hades PS5 game guide video shows an example of Charon optional boss fight. Charon is only a merchant for the vast majority of the game, however there is a chance to fight him – you have to keep visiting his stores until you see a bag of gold behind him. Try to steal it. This will trigger a boss fight on a separate arena.
Charon shoots purple projectiles for the entire fight and their intensity changes later in the duel. Use dodges and hide behind large objects to avoid getting hit. The boss also likes to do large sweeping attacks and 360 attacks – dodge again or attack him from larger distance.
Winning against Charon is awarded with To Charon’s Credit trophy and a membership card which will lower Charon’s prices in the current run.
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Additional info: Unlocking the chance to fight Charon might be tricky. Keep visiting his stores until you spot a bag of gold behind him. Trying to steal that gold will unlock the boss fight. Win the fight to get To Charon's Credit achievement and a membership card granting lower prices for the current run.