For this achievement, you have to kill enemies using the Arbiter or Eryx ONLY. If you soften the enemy up first using any other weapon, it will not count. You can only use your demon weapons the entire time of killing an enemy for it to count.
You'll get some kills automatically by killing enemies that can only be harmed with demon weapons (Hell Knights and Blood Rages). You can easily repeat earlier stages with easier enemies to farm this too if you want, such as Mission 1.
A great farming spot is at the start of Mission 11. The game will load you up in a small area with about 10 enemies right as the mission begins. I suggest using the Arbiter over Eryx to farm. Although it's slow, its power will allow you to mop up quickly. I like the combo of jumping and then using Y in the air to perform an aerial move where Dante throws projectiles down at enemies. You can then reload the checkpoint BEFORE the last enemy is killed to respawn all of the enemies. If you don't reload the checkpoint at the right moment, you'll be loaded into the next check point (which is when the Butcher appears).