The firefly fight in Batman: Arkham Origins takes place in three different stages.
You start off by grappling firefly, when he lands he will throw fire blasts and grenades at you which you will need to evade. Choose to evade either to the left or towards the right when you see flames approaching you.
When firefly is done attacking, toss glue grenades at him and quickly follow these up with some batarangs and then fire your grapple when you see the prompt. If done properly, you’ll be able to get firefly into melee range at which you can begin to give him a solid beating.
Repeat this process and you are well on your way to winning this fight.
During this fight, the camera edge will begin to shift. When this happens quickly, grapple to the exposed bar and run left along the girder.
Jump and glide across this area while avoiding the sloping steel plate towards the right of the platform. Hang from the ledge and then curve around to the left side where you can use your grapple to return to the top of the bridge.
Weave and evade between the cars as you go and then slide under the semi-rig where you can re-engage firefly. Rinse and repeat the same tactics you used before and when firefly is low on health you need grapple him when prompted.
Firefly will take off just before his health reaches zero and will pull you behind him so use counter to evade the obstacles as you move through and you will eventually have won this fight.