Now you get to navigate as Catwoman which is far more different than the differences in fighting style (though not hard to adjust for). She can still run and jump but instead of the grapnel, she just has a whip which doesn't retract. This means that you can latch onto something and swing but then you need to climb up the side of the building. This is actually pretty simple, only requiring you to hit the same button a couple of times. You can aim in the direction you want to climb if you look before you leap. However, you will be rewarded with experience (in the upper left) for timing your leaps perfectly so you make a fluid climb to the top. Make your way NE to Catwoman's home. You'll actually see a Bat Signal above your destination.
On the west side of Catwoman's roof is actually a caged in area that you can hop onto. Go close to one of the gates on top and you can climb down through it and hang from the ceiling. Go over the top of the enemies below and you can drop directly from here for a combat takedown. The enemies are pretty simple but you can use this to practice your whip usage. Hit the LT button to attack an enemy with a whip which will knock them over from a good distance. Once done you can approach Catwoman's window and hit A to get your Caltrops.
Keep heading NE (follow the green marker on your compass at the top). You will soon come to a building crawling with enemies (you'll hear them before you see them). These enemies aren't anything special, dispatch them and then head for the tower in the water by way of the broken bridge. Be careful when you cross just beyond the bridge because there are enemies with guns up here. You can sneak up to take them down silently if you are careful. Use your ability to climb around the side of buildings to your advantage. If you get caught, use your whip to down them and then do a ground takedown to eliminate them quickly without taking too much damage.
Once they are clear, head up the stairs to the catwalk and then you can actually swing down to the underside of it and crawl along. You'll bump strait into a Riddle statue so you might as well grab it and then go forward until you are prompted to climb back up. This will put you on the other side of the locked gate. In the next room, you'll get into a minor fight with only five or so enemies. The most important part is that they act somewhat zombie like which doesn't change how you fight them so much as just being neat. After you finish them, a toxin will flood the room (not a Neurotoxin). Jump up to the ceiling and then climb through to the other side.
Again, once you climb up, you'll be confronted with a slightly larger group of enemies. Just keep your wits about you, there is plenty of space for the fight. There are about 8 or so enemies here. Once you've cleared them, there will be more toxin, another jump to the ceiling, and then another climb around to the top where you will be confronted with even more enemies. The difference in this area is that one of the plants on the wall will occasionally shoot fire balls at you. Try to move the fight along as best as possible to limit the number of shots it gets and remember to watch out when it does shoot.
