This achievement requires upgrading a standard weapon to Enchanted +5. The general procedure would be to have Rickert of Vinheim in New Londo Ruins upgrade a weapon to +5, then to Magic +5, then to Enchanted +5. This would require the Enchanted Ember from the Darkroot Garden and a total of 9 Titanite Shards, 10 Green Titanite Shards, 8 Blue Titanite Chunks, and 1 Blue Titanite Slab.
The easiest way to get this achievement, though, is with the Enchanted Falchion found in the Duke's Archives, which any blacksmith can upgrade to +5 with 7 Blue Titanite Chunks and 1 Blue Titanite Slab.
Titanite Shards and Green Titanite Shards are found in limited numbers as you progress and can be bought from some NPCs. Blue Titanite Chunks can be found in somewhat limited static locations throughout the mid-to-late stages of the game (as guaranteed enemy drops or on corpses). The fifth Black Knight in the Kiln of the First Flame (the final area of the game) respawns and always drop a Blue Titanite Chunk. You can find a Blue Titanite Slab in at the end of a twisting invisible path in the Crystal Cave (use prism stones to make your way across) and another in a chest in the Royal Woods, which is an optional area.
Magic and Enchanted reinforcements use the same upgrade materials. The game only saves when you back out of an upgrade menu, so you can get these two weapon upgrade achievements with a single Blue Titanite Slab and 7 Blue Titanite Chunks if you'd prefer to not have to gather 2 Slabs and 14 Chunks. You'll end up losing the resulting fully upgraded weapon by dashboarding right after the achievement pops (before backing out of the upgrade menu) but you will get your upgrade materials back.
You'll want the Enchanted Falchion from the Duke's Archives, which already has the Enchanted infusion applied, This way you won't have to bother with upgrades to get to that point which would normally require 9 Titanite Shards, 10 Green Titanite Shards, and 1 Blue Titanite Chunk. For the Magic Weapon achievement, you'll need the Large Magic Ember found in the Duke's Archives after defeating Seath the Scaleless, but you won't actually need the Enchanted Ember from the Darkroot Garden since the Enchanted Falchion is already upgraded beyond what Rickert would need the Enchanted Ember to do.
Once you have everything you need, head to Rickert in New Londo Ruins and give him the Large Magic Ember. Start by reinforcing the Enchanted Falchion to +5. Wait a few seconds after applying the final upgrade (which requires 1 Blue Titanite Slab) and this achievement will pop. Again, do not back out of this menu screen confirming that the weapon was upgraded to +5, but instead go to the dashboard and force quit the game, then restart the game and continue. You'll be back at Rickert as if you had never done the Enchanted upgrades.
Now have Rickert "Modify Equipment." The far right option should allow you to revert the Enchanted Falchion to a +5 Magic Falchion. Then choose the option to upgrade ("ascend") the +5 Magic Falchion to +6, which requires the Large Magic Ember. Back up to Rickert's main menu and choose to Reinforce Weapon, then upgrade the +6 Magic Falchion up to +10, at which point the Magic Weapon achievement will pop. You can dashboard here if you'd prefer to save your Chunks and Slab for something else.
As always, refer to
http://darksouls.wikidot.com for specific information relating to items or locations.