Dark Souls 2 - How to upgrade your weapons to the max
Here's how to really hurt your enemies.
"Supreme Weapon" Objective / Trophy Guide
To unlock this trophy (but also to have more powerful weapons in your inventory) we will have to bring a weapon to level +10. To unlock the achievement I recommend upgrading the "fire longsword" found right at the beginning of the game, but remember that you can do this with any weapon that requires titanite for upgrades.
Here's what exactly it takes to fully upgrade a weapon:
Level +1 = 1 Titanite fragment
Level +2 = 2 Titanite shards
Level +3 = 3 Titanite shards
Level +4 = 1 Large Titanite Shard
Level +5 = 2 Large Titanite shards
Level +6 = 3 Large Titanite shards
Level +7 = 1 piece of Titanite
Level +8 = 2 pieces of Titanite
Level +9 = 3 pieces of Titanite
Level +10 = Titanite slab
Where to find the Titanite
You will have no trouble finding them scattered around the game world Large fragments and fragments of Titanite.
About the pieces of Titanite instead, the easiest and fastest way to find them is to join the Noisy Pact in the Bell Tower of the Moon (follow the guide to the Noisy Pact for more help). You will have one every time you defend the tower from an invader by killing it.
Finally, to find the Titanite slab, you can take the one behind a secret wall in the Forest of Giants, or follow one of the many videos on "Titanite Slab" farming on youtube (link).
As you collect the required Titanite you can use it at Majula's blacksmith to upgrade your weapon.