To get this achievement you must upgrade a weapon to +10 by reinforcing it through a blacksmith with titanite.
You need a total of 6 titanite shards, 6 large titanite shards, 6 titanite chunks, and a titanite slab. Also, each upgrade costs souls, which depends on the weapon and level.
+3 - takes 6 titanite shards to this point.
+6 - takes 6 large titanite shards to this point.
+9 - takes 6 titanite chunks to this point.
+10 - takes one titanite slab.
You can reinforce your weapon at Blacksmith Lenigrast in Majula, Steady Hand McDuff in the Lost Bastille, and Weaponsmith Ornifex in Brightston Cove Tseldora.
Titanite shards are easy to come by, particularly as items found in lower level areas, can be bought from Lenigrast, and Chloanne has an unlimited amount of them to sell.
Large titanite shards are easy to buy, McDuff sells an unlimited amount, as does Chloanne. They are also dropped by various enemies such as Old Ironclads (turtle guys) in the Forest of Fallen Giants.
Titanite chunks are more difficult, Chloanne sells an unlimited amount after the final boss is defeated. They are also a rare drop from Gyrm Warriors in the Doors of Pharros. The fastest way to get them is to join the Bell Keepers as you receive one with each successful invasion.
Titanite slabs are very rare, but not quite as bad as in the first game. Chloanne sells one (late-game), another is inherited from McDuff, they can be given by Dyna and Tillo in Things Betwixt, and one from the Pharros contraption underneath the ballista room in the Forest of Fallen Giants. Another is dropped by the dragonrider in the Undead Crypt. You have a chance to receive a titanite slab when defeating an invading Bell Keeper grey spirit.
The Bell Keeper covenant also gives a chance for a titanite slab for defeating a host (instead of a chunk), and you also receive one for reaching rank 1 (10 kills). Stone statues near the King's Gate bonfire in Drangleic Castle may drop slabs, allowing to farm slabs. Thanks to Catatonic Nali for this information.