In this chapter, Batman needs to rescue Gotham City's intrepid reporter, Vickie Vale, from a helicopter crash courtesy of the Joker.
Gotham City Police Department
After the boss fight with Mr. Freeze, the good doctor will give you his Freeze Blast weapon, which will allow you to block steam pipes. Use two of them on the pipes on your left and leave the GCPD Building out the back. You should have levelled up by now: I highly recommend getting the Firearm Disruptor upgrade here, as it will be a lifesaver in some of the later levels, particularly Wonder Tower.
Once you head out the back entrance, you're treated to a horrifying (and unskippable!) cutscene of Vickie Vale's chopper crashing into the Gotham Freeway. Head towards the scene of the crash.
Rescuing Vicki Vale
From a gameplay standpoint, this area takes the mostly-optional sniper neutralizing from earlier and makes it mandatory. You won't be able to rescue Vale until all four snipers covering the crash site are unconscious; you can use the Firearm Disruptor to temporarily avoid getting shot, but even those disarmed snipers need to be physically taken out.
The strategy in the video is the best I can find. Use the Disruptor on the two snipers to the left, before taking care of the two snipers past the billboard on your right. The snipers on the left will see you, but their guns will be useless. Zip up to a vantage point and take them out, then head down to the burning wreckage and walk up to Vickie Vale to rescue her.
Back to the Mile
Once Vale is safe, a short cutscene plays, and then it's time to head back to the Steel Mill to confront Joker. Still more snipers await you here, but you only need to deal with the ones actually guarding the Mill. The two snipers near the entrance of Amusement Mile, for instance, are irrelevant.
Your first priority is to try and get into the Steel Mill the way you did before, but the furnace is too hot to get inside. Oracle will then point you to a back entrance, where the really problematic snipers are.
Industrial District: Infiltrating the Steel Mill
For this section, you need to be a bit more aggressive. You will be spotted at least a few times, so make sure you have decent armour upgrades before heading to Amusement Mile. Focus on the snipers first, and save your Disruptor for some of the armed thugs near the door. After the two snipers are down, you'll need to focus on the armed thugs a little lower down. There's no real way to do this stealthily without a lot of waiting and pitch-perfect movement. You can make do by Glide Kicking one thug, knocking them out, then zipping up to a vantage point, repeating the process until only the thugs guarding the door remain.
There's no way to deal with the thugs near the door except a straight-on brawl. Since they're all armed, liberal use of the Remote Electrical Charge is recommended. Once the area is secure, head through the door to enter the Steel Mill for a nice little platforming sequence.