In accordance with the information received from Alfred, you now need to reach the roof of the Ace Chemicals building. Face towards it #1, hold down A and move the analog stick. The main hero should automatically jump towards the ledge visible in the distance and grab it #2.
Move to the right, thanks to which you will reach a new ledge #1. Climb up and afterwards use two new ladders. After reaching the higher platform, press and hold the right trigger to crouch #2 and move forward.
Approach the ledge and following the instructions, press the right trigger and A at the same time. It should cause Bruce to drop down and grab the ledge #1. Move to the right and you should soon reach a place where you can climb back up #2.
Move forward a bit and crouch once again #1 to be able to move on. Use the ladder on your way and after reaching the new ledge, hold down A and jump towards the platform visible in the distance #2.
Ignore the flying machine and continue climbing up, eventually reaching a ladder leading onto the top of the building #1. Look for the package from Alfred and interact with it by pressing A #2. Bruce Wayne will put on the Batman suit.
You will have to solve an easy mini-game involving the Cryptographic Sequencer. Start by using the left analog stick to find two green points #1 #2 and spend a few seconds on listening to a short recording.
In the end track the orange area in the upper right corner #1. Hold down A and wait for the decoding process to end #2. From the new recording you will learn that Catwoman is being held hostage by Harvey Dent (aka Two-Face) in the Solomon Wayne Courthouse. Saving her is your next objective.