For the most part, Purifying Salts are associated with the Monster Arena sidequest, although they can also sometimes be stolen from Warrior Monks and Fallen Monks. As to the Arena, they can be stolen from Abadon and Hornet (the latter case is less frequent, though). You will also automatically receive 99 Purifying Salts at the Arena after capturing at least four of all Dragon-type enemies in the game.