I've completed Arkham Origins, and am playing through New Game Plus. I'm at the Firefly fight on the bridge, and can't recall how to win. I'm at the point where he's basically defeated, and Batman says "I should grapple onto Firefly".

I grapple on, and we fly around the bridge a bit. Batman falls off, and I grapple on again. We fly a little higher, and Firefly turns around and fries me with his flamethrower. I've tried dodging, countering, attacking, grappling, and just watching, but all end with me dying

How do I avoid getting fried, and how do I defeat Firefly? I don't recall having this issue the first time through. Is this a New Game Plus addition, or is it just easier the first time through?

Googling for the answer gives me things like this:

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.

which doesn't explain what to do when he shoots me with a facefull of fire.

This video was shared in chat, but doesn't quite address the issue. At about 9:30 in the video, Batman falls off of Firefly, and I have to grapple back on. A few seconds later, Firefly turns around and shoots a bunch of fire....Game Over.