Paul Dano’s Riddler seems to be directly targeting Robert Pattinson's Dark Knight in The Batman, and there are a few likely reasons why. Historically, the question mark villain has been one of Batman’s sillier foes, but the version featured in the Matt Reeves film is far darker and more twisted. The Batman’s Riddler is more like the Zodiac Killer, and his primary target seems to be the Dark Knight himself.
Through both The Batman trailers, the Riddler has appeared mostly in obstructed shots, with his true face remaining in shadow. From the riddles he’s left at the scene of his serial killings, it appears that he’s trying – or at least believes he’s trying – to reveal some sort of deep-seated corruption at the heart of Gotham. He’s also seen leaving notes addressed to “The Batman” in particular, showing that his main focus may be less on Gotham as a whole, and more on its Caped Crusader.
The simplest explanation for Riddler’s interest in the Batman is that he enjoys having an adversary of similar intelligence. In the comics, the Riddler prides himself on being able to outsmart even the most capable opponents, and no one is more capable than the Dark Knight. Like the Zodiac Killer, The Batman's Riddler seems to enjoy making a public show of his killings, which indicates he carries the same ego and desire to prove himself the best as his comic book counterpart. Because Batman has established himself as the most dangerous enemy Gotham City's criminals have, it would make sense for the Riddler to single him out. After all, if he can outsmart Batman, he could easily be seen as the most powerful man in Gotham.
It’s also possible that the Riddler sees Batman as a dishonest figure in Gotham – someone’s whose proclaimed interest in protecting the innocent and punishing the evil is simply a guise to hide his own abuses of power. Pattinson's Batman is clearly a brutal and deeply troubled person, which means the Riddler might be able to turn public sentiment against the Dark Knight by exposing his true nature - something he could see as a victory and a point of pride.
This could lead to a greater and more interesting potential goal for The Batman: he knows that Batman is Bruce Wayne and is trying to expose him. Many of the Batman comics’ most notable storylines characterize Bruce’s father as being a key part of Gotham’s decline. As the head of Wayne Industries, Thomas Wayne was instrumental in the city's economy, including the ways it collapsed on the have-nots. If The Batman’s Riddler truly believes himself to be on some kind of noble quest to root out corruption, he may be trying to punish Bruce for the sins of his father. This idea isn't entirely without merit; the phrase is included as part of the villain’s elaborate riddle in the second trailer for The Batman.
Whatever the Riddler’s true motivations are for tormenting Batman, his campaign may push the Dark Knight to his absolute limits. The most recent The Batman trailer includes a shot of Batman interrogating a prisoner who appears to be the Riddler with less than stellar results. With the killer apparently making his villainous intentions public with livestreams to the population of The Batman’s Gotham City, hundreds of thousands of people will be watching Batman’s every move. It should be exciting to see the two characters clash on screen when The Batman releases on March 4, 2022.