To unlock the Pyro trophy in Borderlands: Game of the Year Edition, you will need to kill 25 enemies with incendiary weapons.
Incendiary weapons can be identified by the red fire symbol in your inventory (similar to the trophy art image). You can also do fire damage by shooting the red barrels.
When you use an incendiary weapon, red numbers will appear around an enemy to indicate that you are causing incendiary damage.