Righteous Punishment is a dye for Ghost Armor. It is tied to a choice you make during "The Tale of Lord Shimura" in the main story. Like every dye it only changes colours.
Play "The Tale of Lord Shimura". The dye you get depends on a decision made during that tale, and the other Ghost Armor choice dye goes with the other option.
You get this dye by choosing "Kill" when the tale asks you to decide Lord Shimura's fate.
Once unlocked it shows up as a colour option for Ghost Armor, so you need that outfit to use it.