Kill It With Fire!
There is no mob named Burning Souls, instead you have to kite the Soul fragments, spawned during the "Twilight Phase", over a patch of fire so they get a debuff and kill them while they have it.
The title of the achievement could be a reference to a Dragon Ball Z Abridged episode where Bulma exclaims "Kill it with fire!" after seeing Zarbon transform.
- Patch 4.0.3a (2010-11-23): Added.