This achievement has had some people become frustrated. It is believed by some that you must kill human enemies only. Here is the list of weapons you must use. My opinion is strong to say that killing with any blade is fine. This is because there is an Overseer Blade and an Assassin's Blade. Both of them are found in the Flooded District but not both of them can be obtained at the same time. Also, there is a dueling pistol during Mission 5 that you can only shoot during a duel while completing a side objective. I also do not believe this is required.
City Watch Sword - This is obtained in Coldridge Prison right after you escape.
Corvo's Folding Blade - Automatic and is what you use almost the full game
Overseer Blade/Assassin's Blade - These are found in Mission 7: The Flooded District but cannot both be equipped, therefore my conclusion they are not part of the list.
City Watch Pistol/Corvo's Pistol - You will find this in the prison and beyond, extremely hard to miss. Corvo's pistol is just the upgraded City Watch pistol.
Upgrade: Explosive Bullet - This is an upgrade that is only obtained when discovering the required blueprint. You buy the ammo and it is a separate icon than regular bullets.
Necessary Blueprint locations:
(Note: Picking up a blueprint with multiple locations, will make it disappear from all locations)
Mission: House of Pleasure
Item: Incandescent Paste; Incendiary Bolt Blueprints (Location 1)
Location: Use the valve-controlled door located within the Distillery to reach the blueprint
Mission:Lady Boyle's Last Party
Item: Spiked Grenade Housing; Sticky Grenade Blueprints (Location 1)
Location: Before entering the Mansion through the side entrance (which enters into the main hall and staircase), take a left and enter a side door into a guard's room to find the blueprints on a table.
Mission: Return to the Tower
Item: Small-Scale Combustion Refinement; Explosive Bullets (Location 1)
Location: Once you're inside Dunwall Tower, check the rooms on the second floor, and you will find this in the General's office.
The Flooded District
Item 1: Spiked Grenade Housing; Sticky Grenade Blue prints (Location 2)
Location: Inside the Thug's basement with a partially destroyed passageway
Item 2:Incandescent Paste; Incendiary Bolts (Location 2)
Location: In the lower level cellar near the exit from the Gateward Tunnels.
Item 3: Small-Scale Combustion Refinement; Explosive Bullets (Location 2)
Location: In the crashed railcar you pass by as you exit the rail station, and just before reaching the main area with Daud, and tons of Assassins.