After the fight starts, start attacking the Copperhead clones that gather around Batman. Just like during the fight a couple of moments ago in the Concealed Room, you should especially pay attention to the enemies with knives and remember about the necessity to hold down the counter-attack key/button. Apart from that, be on a lookout for opportunities to respond simultaneously to attacks of one that one character (the blue markings above the heads of several characters) Occasionally, it may happen that Batman is grabbed by Copperhead and you need to tap rhythmically on the interaction key/button to free yourself.
Just like in the case of the other boss battles, try at the outset try to avoid losing too much health, because you may run out of them before the end of this fight. Do not attempt to target the actual boss while fighting the clones because he will be "unmasked" after the end of each successive phase of the battle. Then, land quick combos in an attempt to decrease the boss's health bar, which you can see in the corner of the screen.
After she loses around 2/3 of her health bar, Copperhead will start to pull off a very quick sprint attack, which you of course need to avoid at all costs. Once you notice the flash of light shown in screenshot 1, perform a quick dodge to the side, should will allow you to keep the current state of your health bar.
Resume the process of attacking the clones and remember that you still need to keep a careful eye on the environment and perform flawless dodges whenever you notice the flash warning you of the imminence of the actual boss. Keep doing that until all of the clones are defeated, which will reward you with the antidote that will restore you to full health.
The only thing remaining for you to do is finish off the main opponent and so, approach Copperhead and press the standard attack key/button which will result in a cutscene of the boss's capturing.
[Character Profile Updated: Copperhead]
[New Character Trophy: Copperhead]