Select the newly-acquired Remote Claw from the inventory and aim it at one of the interactive points above the arena (the above screenshot). Note that both points have been connected with a rope and, thanks to that, you can grapple it with the hook. Using the rope, make it over to the balcony with door to the Penguin's office. Unfortunately, you will fail if you try to make it past the door but, you will have another talk with the Penguin instead.
[New Character Trophy: Penguin]
[New Character Trophy: Candy]
Jump down and walk towards the ship's exit so, take the arena's Southern door to Deck 1. After you have reached the partially flooded corridor again, activate the hook again in order to extend another rope. Jump onto the rope and, after you have reached the opposite ledge, resume along your way. Along your path, listen to the conversation with Alfred and, after you return to the Gun Shop listen to Anarky's speech also, who has a side mission connected with him ( the mission has been described in a separate chapter of this guide). You can now leave The Final Offer.
[Character Profile Update: Deathstroke]
[New Character Profile: Anarky]
The place that you currently need to reach is the building located in the central part of the Coventry district in the Southern Arkham. Since it may happen that the game will remove the marker from the map, the location of your destination has been marked on the map in the above screenshot.
Your destination point is a relatively small roof with three policemen on it. I recommend that you grab onto the edge of the roof and throw one of the policemen off. Only then, take to the remaining enemies and deal with them in a direct fight. After you have won the fight, select the Cryptographic Sequencer from the inventory. Just like earlier during the campaign, place the crosshair in the orange circle and decode the transmission (press and hold down the appropriate key/button).
Go east now, i.e. towards the next two policemen who have been marked by the game. I recommend that you attack these ones by surprise as well, especially that grabbing onto the edge below them (the above screenshot) will allow you to throw over the balustrade both of them at the same time. You can now take the entry to the Lacey Towers.
Follow the linear corridor to reach Sionis' Safehouse, i.e. a crime site, after several moments, which requires a careful inspection. You should, of course, start with starting the evidence scanner and scanning the victim deemed to be the Black Mask (you need to press and hold down the key/button that the game prompts you to) to analyze the left hand fingertips.
Turn around and approach the chandelier to scan the woman hung here, thus learning her personals.
Another area that can be scanned is the floor near the chandelier with traces on it. Performing a scan here will allow you to determine the how the fire spread all around the apartment. Return to Black Mask's corpse. Scanning it once again will start another reconstruction, this time concerning the circumstances of the man's murder.
Approach the woman hanging down from the chandelier again and scan the corpse again. Also in this case, you will need to determine the fired bullet's trajectory. turn around and locate a new trace to the right of Black Mask's corpse. It is going to be fingerprints that can be subject to examination. Remain in this area and locate the shoe polish smears and scan them.
Take a look around the site for possible DNA on the floor, connected this time with the destroyed table. After you see another reconstruction, start holding down the keys/triggers for adjusting the reconstruction. Follow the red line, which will take you to the balcony door. You will find here a fragment of clothing, which you of course need to scan.
Go now towards the apartment's exit but, after you take the stairs, turn right and examine the counter on the right. Press, and hold down the appropriate key/button after you target the DNA trace shown in the above screenshot, thanks to which you will see another reconstruction.
Finally, find the cell phone lying on the floor. Examining it will allow you to read an important message. Watch the final version of events and listen to the conversation with Alfred.