how do i unlock conqueror's haki sailor piece without wasting hours?

as far as i know there's no quest for it, it's a roll. you get to the point where the game can hand it to you and then it rechecks every so often, and you either get the notification or you don't. that's why every guide you find says something different. nothing you do raises the odds, so don't burn a whole day grinding specifically for it - just play and it turns up.