The fights against the Firefly take place during the Gotham on Fire side mission, i.e. the one concerned with fire stations that are being set on fire. In total, you need to defeat the Firefly three times, where each one of the fights is identical with the previous one. This has been described below.
All of the three encounters with the Firefly take place each time you manage to extinguish the fire of the fire station that he has set on fire. After you regain control of Batman, follow him in the car. It is not too difficult, although the opponent is deploying explosive and flaming traps on the road. Keep within the medium distance of the Firefly and remember to use your brakes for effective 90° turns.
Do not attempt laying any sort of fire on the Firefly, remain in the batmobile's pursuit mode. You need tor the opponent to run out of fuel in his jetpack (the meter in the upper-right corner of the screen). As soon as this happens, cut down the distance and wait for the message about the option to eject Batman and perform a special takedown in mid-air (double-tap the jump key/button).
If everything went according to the plan, Batman reaches Firefly automatically. The only thing you need to do now is use Beatdown, so you need to start tapping the melee key/button.
Do the same in the case of the remaining two fights with the Firefly.