To get this achievement you must kill 25 enemies (skags, bandits ect) with weapons that have a fire element.
These weapons have a red fire sign in the inventory menu.
Red numbers will come off enemies if they are impacted by fire damage. Fire damage is like other elemental damage in the game in this is causes damage over time. The enemy does not have to die as a result of the fire damage however.
You can check your fire kill count in the challenge menu, go to the quest screen and press Y.
You can also use barrels for this achievement. Fire barrels are red.