This mission is added after you tracked down the militia vehicle that abducted Oracle and reconstructed the crash site where Oracle threw a scrambler for you to find. Head to the rooftop to find the burning Batman symbol. Talk to Azrael and you'll control him as he proves himself against a mob. You need to complete the challenge without getting hit to prove you're worthy.
Azrael's next location is in Founders' Island, north of Port Adams. Like before, you have to defeat all enemies without getting hit. He's using the same combos and skills as Batman so take out the smaller fries first before beating down the brute.
Azrael's next location is in Chinatown. In this challenge, you'll have to deal with a medic and a charged up militia. You have to avoid touching the electrified guy; you can remove the electricity from him by using the Batclaw. Make sure to take out the medic as fast as you can as well.
This intel becomes available only after Harley Quinn appears in the main story. Head to Lady Gotham (the lone island in the middle of the city and make your way to the top to find the burning bat symbol. To pass this test, you have to ensure that Azrael doesn't get hit by the elite militia swordsmen.
Next, head to the Clocktower to analyze Azrael's unusual neurological activity through the batcomputer. After playing Azrael's memory, replay the footage and examine the parts with strange symbols to complete the waveform and reconstruct the order's real message.
Azrael will appear inside the Clocktower and you'll have to control him. You'll be forced to get the sword on top of the lockers. As Azrael, you'll have to choice whether you'll kill Batman or not. If you choose to break the sword, leave the clocktower through the elevator to complete the mission and close the case.