Noble Yggralith Scales are prime materials in Xenoblade Chronicles X. They are given out as rewards for taking RP from Yggralith Zero after the Nemesis is defeated or flees. They are used to craft the True and Infinite BLADE Wear series.
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This material is now in limited supply as the only method of obtaining it is via the limited supply of Reward Tickets obtained from fully completing the survey of Mira.