This Achievement is for upgrading a weapon to +10 status. I used the fire longsword that can be found pretty close to the beginning of the game. You're going to need 6 titanite shards, 6 large titanite shards, 6 titanite chunks and a titanite slab to get this done. Your weapon can be upgraded by the blacksmith in Majula, providing you bought the key to his house off of the hag merchant, Melentia.
When it comes to collecting the materials, large and small titanite shards are easy enough to come across. Titanite chunks can be gained by joining the Bell Keeper's covenant in Belfry Luna. You'll earn a titanite chunk for each "invader" of the tower that you successfully kill. As for the slab, it can be find behind a secret wall next to a Pharros' Lockstone spot in the Forest of Giants. This is right below the area with hollow soldiers manning a few ballistae, close to where Pate can be found, and a little after the second bonfire.