Zartan never trained as a ninja. He apprenticed with the Arashikage's clan's blacksmith to get close to the clan (he helped forge a sword that Storm Shadow would get in the silent issue titled "SFX"), learning the secret of katana making (hard metal maintains its edge, but breaks easily; soft metal has no edge, but doesn't break), folding the metal over and over until the perfect blade was created.
While he had some skill with a bow, Zartan had to use sound amplification equipment to replica Storm Shadow's "Ear that Sees" technique to murder the Hard Master.