Delicate Scales is an Imbuing ingredient needed to imbue the Use Best Weapon Skill property onto weapons. It can be found as loot on creatures living in the Cavern of the Discarded.
They also can spawn in the backpack of fishermen. There is no special place to seek for these, any location that yeilds a fish can spawn a resource gem. The skill requirement to be able to fish these up are still unknown. An educated guess would put the requirement to 80, the same as for White Pearls.