What is the easiest most efficient way to farm Shadow Scales?

Create Worm Food and activate it in the corruption. Build a nice platform to stand on and kill Eater of Worlds (which spawns when you activate Worm Food). You'll get LOTS of shadow scales.

The only way to get shadow scales is by defeating the Eater of Worlds. Here are some strategies to defeat him:

• Defeat the Eye of Cthulhu by crafting a Suspicious Looking Eye at a demon altar(takes 10 lenses from Demon Eyes). Using this item will spawn the Eye of Cthulhu and when you defeat him(suggest using lots of flaming arrows with the best bow you have), he will drop Demonite Ore. You can use this to craft powerful weapons.
• You can also mine to find Demonite and other ores to craft more powerful weapons and armor, etc.
• Adventure in the corruption. If you mine in the corruption(do not suggest until after you have defeated the Eye of Cthulhu and gained more equipment) you will find Shadow Orbs. Smash these with hammers or explosives(from pots and the Demolitionist NPC). The first one you smash will give you the Musket and 100 musket balls. This is a good weapon at this time in the game and will allow access to the Arms Dealer NPC. Smashing more orbs can give you powerful weapons. However, every third orb you smash will spawn the Eater of Worlds.
• If you are lucky and get the Vilethorn from a Shadow Orb, it's great against the Eater of Worlds.
• You can also spawn the Eater of Worlds using Worm Food. This is crafted using 30 Vile Powder(crafted from Vile Mushrooms found in the Corruption at a placed bottle/alchemy table) and 15 Rotten Chunks, a common drop from Corruption enemies such as Eater of Souls, at a Demon Altar.
• If you plan to use Worm Food, make a large platform above ground to fight on.
• Summon the Eater of Worlds. Using the Vilethorn, Musket, demonite weapons, etc. and good planning, you can probably defeat him first try. If not, his body sections will each drop some demonite ore and shadow scales that you can use to craft the Nightmare Pickaxe, Shadow Armor, and other things.
• Once you have decent enough equipment, you can farm the Eater of Worlds for lots of money, demonite ore, and shadow scales.

Good Luck!