In this mission, you’ll need to head to Blackgate Penitentiary, where Harley Quinn apparently has some information that Batman requested.
Before leaving the Belfry for this mission, open the map and find Blackgate Penitentiary, which is just to the west of the Belfry, on Blackgate Island. Track Harley’s location, then exit the Belfry and make your way to Blackgate on the Batcycle. Once there, sneak past the guards at the gate and make your way down the stairs to the left.
Follow the diamonds as they lead you to the bridge’s support platforms — hold /to jump across the gaps, and then grapple to the far side of the water. Head left around the bridge’s support column, and once again follow the diamonds as they lead you to a small drainage pipe. Hold /to enter it, and — after a loading screen — continue forwards, turn right at the wall (2), and squeeze through the gap ahead. On the other side, turn slightly right and hold /to climb the wall with wooden boards (2).
Just ahead you’ll see a chest. Open it, and then turn right and climb up onto the ledge. Continue forwards and drop down, then grapple to the higher ground (1). Go straight and bear slightly right, and you’ll see a concrete ledge you can climb up (2).
Then, turn left and grapple up the next concrete ledge, just around the corner on the right you’ll find a control panel. Interact with it, and the door will open. Step through and drop down to finally enter the penitentiary. Press to crouch, and duck past the girder so you can drop down into the room with the Blackgate Security Guards. Go left and vault over the low concrete wall to sneak past the guards.
Follow the white diamond through the doorway, around the large pillar, and to the double doors. Open the doors, and you’ll encounter a trio of inmates. Take them out, then continue forward to the metal door ahead. There’s a small, hard to spot panel on the wall to the left of the door that you’ll need to interact with in order to proceed.
Head through the door, and then you have two options: go past the stairs to the railing and perch on it, and you’ll be able to do an aerial on one of the inmates below. Alternatively, you can go down the stairs and try to sneak behind the inmates, potentially getting a stealth takedown or two in. Either way, you’ll need to defeat them all to continue — make sure you focus on avoiding damage to get the bonus rewards.
Once they’re all taken care of, head to the corner of the yard where the white diamond is, and the metal gate there will open. Continue up the stairs and turn right, and Harley’s cell will be the first one on the right. Walk over to her cell until you get the Talk to Harley Quinn prompt, hold /, and a cutscene will play. When it ends, turn left from her cell and head towards the white diamond in front of the now-opening door. Continue through, turn left, and then you’ll have to immediately turn right. Look up and grapple to the platform above you — you’ll find a chest here, and then you can attack the inmates from above. Defeat all three, then squeeze through the door they were in front of.
Turn right and head out into the yard, and defeat the five enemies there. Make sure you evade the shotgunners attacks, and also note that you’ll need to use heavy melee attacks (hold /) to guardbreak any time you see the icon while attacking. Once all the enemies are defeated, head towards teh doorway indicated by the diamond, and open the door there. Continue following the diamonds, and you’ll soon get a short cutscene and then have to face the Godmother.
Focus on avoiding her attacks, and once your Momentum bar is full, hold and press / to use a Piercing batarang attack — this will allow you to interrupt the Godmothers attacks, and briefly stun her to allow you to get some free damage in. Once she’s down, two guards will enter the room, and you’ll need to take the both down as well. Then you can follow the white diamond up the small ledge — use the control panel to the left of the door to open it, then head through.
In the next area, you’ll see some guards and inmates fighting. You can join in the carnage for some rewards, or just grapple over them into the elevator shaft.
Drop down into the shaft and then continue forwards — you’ll need to crouch — and turn right to enter the ventilation shaft. Follow it until it drops you out into a basement room, where you’ll be able to sneak up on the inmates and take them out silently (if you so choose). There’s a heavy enemy here, so don’t forget to guard break them before attacking. Once all three enemies are defeated, find the doors indicated below and open them.
In the next room, turn left and head down the stairs to enter the records room. Straight ahead on the desk, is a card catalog. Use your AR scanner () to scan it, and then pick up the card from the catalog. You’ll need to go up the stairs to the left of the desk, but first you can interact with an open file cabinet behind the desk to get the first of 4 marked items required for some bonus rewards. Then go up the stairs, and on the first open room on your left, you can open a chest and examine the second marked item.
Then go back out into the hall and look left, and use your AR scanner again. You’ll see a File Archive — analyze it, and then you’ll be able to walk over and grab the file from the drawer.
Exit the room with the File Archive, turn left, and go up the short staircase. In this room full of junk, you’ll find the final two marked items you need to examine for your bonus rewards, and then you can jump out of the room and follow the diamond, which will lead you out the way you came in. Open the doors once again, and head straight into the basement. In the far right corner of the basement (where the diamond is leading you) you’ll need to hold / in order to climb up into the ventilation shaft.
Continue through the shaft, and once you exit it, follow the diamonds back into the elevator shaft and grapple up to exit it. Once you’re out of the shaft, you’ll be perched over a group of inmates — you can choose to fight them, or you can just follow the diamond, exiting the room via the doorway on the far left side of the room. Make your way around the large column, then open the doors on the other side. Continue through the burning hallway and you’ll be back outside.
Go down the stairs, cross the yard, and go up the staircase on the other side — you’ll find Harley’s cell on your right at the top of the stairs. Once again, walk up to her cell and hold /to speak with her, starting another cutscene. When it ends, you’ll need to follow the balloon through the doorway and down the hall — again, you can ignore the enemies here if you like. The balloon will go out a small window — grapple up to it to start another cutscene. Once it ends, you’ll have to beat up basically everyone in the yard, with a bonus available if you can do 6 perfectly-timed evades.
You’ll have to defeat another Heavy enemy during this fight — don’t forget about holding / to guard break them. Once you finish off all the enemies in the yard, yet another cutscene will play, and you’ll find yourself back on the bridge that leads to Blackgate. You can now fast travel back to the Belfry. To complete this mission, you’ll need to Open Harley’s book, which is sitting on some boxes near the evidence board.