Here's something I would absolutely
love to see in the sequel, as a nod to films along the lines of Se7en and Silence of the Lambs. Have the Joker run rampant on a killing spree in Gotham, with the Clown Prince of Crime randomly disposing of his victims in seemingly freakish and unconventional ways completely devoid of patterns and logical reasoning, thereby leaving Batman nothing but dust as to clues of the Joker's next possible victim.
And as Batman, despite being ever the detective, is now locked in his cave, hopeslessly glaring at the forensic evidence gathered from the previous murders. Confused and lost, struggling to try and save the next unfortunate soul that tickles the Joker's fancy, he sets out for further and more detailed examination of the murder sites. On his way, Batman intercepts one of the GCPD patrol car transmissions :
"Alert all units. The serial-killing madman has been apprehended in the Gotham Financial District. All units in closest proximity prioritize escorting the suspect to Arkham."
"Something's not right", thinks Batman. "An usual killer this lethal, brilliant and elusive can't be caught by typical means..." Nevertheless, he keeps his eye on the police communications anticipating, lest something go awry.
A couple of hours later after checking out the murder sites, Batman sees the signal lit up the night sky. Looks like Gordon wants to talk to him.
"You're never gonna believe this", quips Gordon "we got tipped by an anonymous source as to the killer's whereabouts and turns out that our guy voluntarily turned himself in. Looks like he's taken quite a fancy to you, demands to talk to you alone at Arkham. A couple of interrogators tried sizing him up a bit but ended up in the infirmary. Stabbed one with a pencil in the eye, burnt the other's face with some kind of acid he pulled out of nowhere and burst into hyseterical laughter. Had to move him to maximum security. We couldn't get a word out him."
And so have Batman and Joker talk face to face in a huge empty circle chamber at Arkham, with the Joker shackled up in chains. Would make for a damn interesting conversation, with the Joker admitting his strange, sadistic fascination with the Batman and a truly nasty surprise waiting in store for him at the end of their little "chat".