The boss battle with Firefly will take place in three parts over its course. The first will be on top of the bridge when you first encounter him, the second will just be some running through flaming wreckage, and the third will more or less just be a repeat of the first part of the battle.
When Firefly is flying back and forth, red lines will appear above his head to let you know that he is going to attack. The first round is the flamethrower, so dodge roll to one side to avoid it. When he isn’t firing, you can either keep tossing batarangs at him to daze him and then pull him down with the batclaw and give him some up close and personal love, or you can hit him with a glue grenade and then chip away at him with batarangs while he’s stuck. Either way, you will hurt him till about halfway where he will torch the bridge and force you to run.
Head through the burning bridge, grappling where necessary until you reach the top of the bridge again. Run to the right and then towards the top of the screen across a blue car. Then make your way left and slide under the truck there. Once you do, the final part of the battle will begin. Instead of just using a flamethrower, Firefly will also toss down grenades.
Both attacks are easy enough to avoid, so keep dodging and tossing batarangs. Use the batclaw when Firefly is dazed and eventually when he is near death, he will light up the bridge with flames and you will then need to use the grapple to grab Firefly and end the battle.
For more tactics here's our full Batman: Arkham Origins boss guide!