This achievement is obtaned by getting a best weapon by Greystones.
To be able to start upgrading by greystones your weapond need to be at least +3 standard weapon. Weapons can be strengthened by Greystones up to a maximum of level 5.
Below are weapons that require the lowest ammount of ore to get final upgrade:
(Shard/Chunk/Pure) Greystones required
Iron Knuckles: Dropped by Miners (Fist) in Stonefang Tunnel (15/6/1)
Short Sword: Sold by Blacksmith Boldwin for 1,000 souls each (20/7/1)
Best places to find Ores:
Greystone shard: Dropped by Rock worms in 2-2 Archstone
Chunk of Greystone: Dropped by Rock worms in 2-2 Archstone (Rare)
Pure Greystone: 2-2 Archstone, show Scirvir a Dragon Bone Smasher. Pure white tendency.
Alternatively a huge ammount of greystone ores can be obtained from Crystal lizard in Archstone 2.