Gain access to the penthouse - East tower | Main storyline Batman: AO Guide

You need to charge the generator

Locate a small catwalk close to the security room that you have just visited. First, use the hook, and the newly-acquired Shock Gloves afterwards (by holding down the interaction key/button), which will start the portable generator and set the entire structure into motion. Wait for the catwalk to change positions into a new place and use the hook again, this time to grab onto the interactive ledge high above.

The window

Look up again, aim at the opened window and use the hook to reach this place, which as a result will take you to the East Tower - 10th Floor. Start exploring this floor, listen to the conversation with Alfred and reach the blocked passage separating Batman from another group of bandits. Also here, you need to use the shock gloves, to charge the control panel built into the wall on the right.

Shock gloves will help you win fights, especially the more demanding ones

Go towards the abovementioned group of bandits and perform a slide under the only, partially-lifted gate. Attack the enemies and keep an eye on the shock gloves gauge that you can see in the upper-left corner of the screen. Each successful attack charges the bar and, after it is fully restored, the possibility to use the gloves in battle becomes available.

You need to escape quickly from the roof of the first elevator

After the victorious fight, listen to the Joker's speech and go to the 10th Floor - Laundry Room. Select here the claw from the inventory and use this gadget to open the venting shaft. Pull up to the opening and reach a new location with several elevator shafts [East Tower - Elevator Shaft]. Ju8mp down onto the closest elevator and immediately jump onto the neighboring one. This is so, because the first one will soon go loose and go down the shaft.

Grab the bandit next to the elevator shaft

Use the shock gloves on the second elevator's generator and wait for it to reach the new area. Since it will stop under the shaft's exit, use the hook, to reach the region of the East Tower - 19th Floor. Start here by throwing down the bandit next to the shaft, climb and deal with his colleagues. In this case,, defeating the enemies should be very easy so, you do not really have to wait for the shock gloves to charge.

The spot where you need to use the grapple

Ignore the civilians and interact with the control panel located next to the locked gate, by using the shock gloves, of course. Explore the linear corridors to reach, the big opened window. Use the grapple here, to extend the rope, slide down the rope, knock down the single enemy at its end and reach the West Tower - 19th Floor.