In the dark, gritty world that is Matt Reeves' The Batman, the Riddler claims many victims, and kills them in a series of increasingly imaginative ways. Paul Dano's role as the Riddler is one of the most unique depictions of the character that audiences have seen in a live-action medium. Rather than making him a flamboyantly eccentric, question-marked-covered goon comparable to the likes of Jim Carrey's portrayal in Batman Forever, he is instead styled to be a highly-intelligent serial killer. His intellect and creativity comes to the forefront in the manner of which he murders his victims.
The entire plot of The Batman features an early-career Batman (Robert Pattinson) as he works to put a stop to the Riddler's killings, which centered around uncovering and ending the corruption that has been ever-prevalent in Gotham City. As such, Riddler was very careful when it came to choosing his targets. Not only would their deaths further his goal of exposing the criminality of Gotham's elite, but the manner in which he kills them would give him the perfect opportunity to leave behind a brain-teaser for Batman to solve. These are all of the Riddler's victims (and attempted victims), why he specifically chose them, and the meaning behind his methods of killing them.
Mayor Don Mitchell Jr.
The very first person in the film to become a Riddler victim was the acting mayor of Gotham City, Don Mitchell Jr. Within The Batman movie opening, the Riddler silently breaks into his home while he is distracted by a news story involving him on the television. Riddler then overpowers him and bludgeons him to death with what was revealed later to be a carpet tucker. The overall reason as to why Riddler used a carpet tucker as his weapon of choice was not fully realized until the film's end. It turned out to be the final clue to discover Nashton's ultimate plan: to flood Gotham City by destroying the sea-wall that surrounded it. The blueprints for his entire operation were deliberately placed underneath the carpet of his apartment; a detail that Batman unfortunately found out too late.
Due to the fact that all of his killings surrounded political conspiracy, Riddler specifically chose to kill Mitchell as a means of exposing the secrets behind a massive drug bust and the arrest of mafia leader Salvatore Maroni, which Mitchell himself ended up being a driving force behind. As it turned out, Mitchell was assisted by Maroni's gangland rival, Carmine Falcone, who used bribery and other shady dealings to help him achieve the rank of mayor. This is not to mention Mitchell's crimes of infidelity, as it was revealed that Mitchell had an affair with a young woman named Annika Koslov, the best friend of The Batman's Catwoman (Zoë Kravitz), to whom he drunkenly divulged the details of the case. This information sadly led to Annika's demise at the hands of Falcone.
Police Commissioner Pete Savage
Riddler's next victim was Peter "Pete" Savage, the head of the Gotham City Police Department. Riddler's method of killing him was definitely the most harrowing, as it was fairly comparable to things seen in the Saw franchise. Pete was stalked and captured by Riddler, who placed his head in a large cage, inside of which were several rats. Riddler injected Savage with a dosage of rat poison. This attracted the rats, and they killed him by clawing into his face in search of the poison's captivating smell. All the while, the entire spectacle was televised by Riddler for all of Gotham to see. As Batman later discovered, the rat cage itself was the next clue to Riddler's game, as the answer prompted him to search for an informant (or "rat" in slang ) that blew the whistle on Maroni's drug trafficking.
Similar to Mayor Mitchell, Commissioner Savage was also involved in Salvatore Maroni's arrest, and was thus partnered with The Batman's Carmine Falcone, who was later revealed to be the Riddler's aforementioned rat. Falcone used his mafia influence to place Savage in charge of the police department. With his new position of power, Savage (and many other cops on the force) were continuously bribed to turn a blind eye to Falcone's criminal operations, resulting in very few actual well-intentioned cops like Lieutenant Jim Gordon being in their ranks.
District Attorney Gil Colson
Riddler's third target was Gilbert "Gil" Colson, Gotham's district attorney. He went out in full Riddler fashion, as he was used to play a friendly game of questions with Batman. Having been captured by Nashton, Colson was outfitted with a bomb collar, which forced him to quite literally crash Mayor Mitchell's funeral with a car as a means of drawing Batman out. Riddler then used a phone that he had strapped to Colson's hand and proceeded to ask the two a series of riddles, the answers of which were confessions of Colson's own corruption. When he refused to answer the third and final question (who the rat of the Maroni case was), Colson's bomb collar detonated, killing him and knocking Batman unconscious.
Colson was the third and final political figure to be involved with Carmine Falcone, hence the reasoning behind Riddler's choosing of him. Like Mitchell and Savage, he was also involved in Maroni's arrest, leading him to be backed by Falcone in his position as the city's DA. More specifically, Colson was constantly bribed to not prosecute any high-profile criminals (most of whom were on Falcone's payroll), which definitively skewed Gotham City's justice system in the worst way possible.
Bruce Wayne (Attempted)
Riddler attempted to kill Gotham's favorite son, Bruce Wayne, with a mailed letter bomb. Unfortunately for him, Bruce himself was out masquerading as Batman, so his plan ultimately failed, but that does not mean that his attempt didn't cause any casualties. Instead of Bruce opening the letter, it was first intercepted by his beloved butler and father figure, Alfred Pennyworth (Andy Serkis). Thankfully, the resulting outcome did not kill Alfred thanks to his quick thinking, as he threw the letter across the room just before it exploded. However, he was still left horribly injured nonetheless and had to stay in the hospital for some time.
The Riddler's chose Bruce Wayne as a target because Nashton himself was an orphan, living in an orphanage owned by the Wayne family. Bruce's father Thomas developed a substantial charity fund called The Batman's Gotham and its impoverished citizens.
Carmine Falcone
The reasoning behind Riddler's targeting of The Batman's Carmine Falcone is rather self-explanatory. This ruthless mob boss had been the center of all of Gotham City's corruption and was Public Enemy Number One besides the Riddler himself. Throughout the entire film, it was revealed the Falcone had many followers and puppets within Gotham politics, his most well-known ones being Don Mitchell, Pete Savage, and Gil Colson. It really came as no surprise that Riddler had him as a target, considering his twisted crusade to rid Gotham of corruption and criminality. By using Batman as his personal tool of justice, Riddler forced Falcone out into the open after he itted to ratting out his rival Maroni and was thus arrested. This gave Riddler the perfect opportunity to end Falcone's tyranny once and for all, as he sniped the mob boss from his conveniently-located apartment, killing him.
Bella Reál (Attempted)
The Riddler's last target is perhaps his most confusing to many viewers. Bella Reál was a candidate for The Batman's mayor, running against Don Mitchell before Riddler killed him. Bella's motives somewhat fall in line with Riddler's own views on some topics, as she wished to cancel the city's Renewal fund and do her best to put an end to Gotham's corruption. Riddler, however, appeared to disregard this due to his contempt for everyone involved in the world of Gotham's politics, and seemingly wanted to use her as a martyr and symbol of his plan to destroy Gotham.
After his plan to flood the city succeeded, citizens gathered in Gotham Square Garden as a means of shelter. The Garden was also the location of Reál's campaigning event. Hiding out at this event was a group of copycat followers of Riddler that was tasked with killing Reál as publicly as possible, seemingly in a way that sends a message to the rest of the world that Gotham's elite will never not be corrupt, despite Bella's selfless goals as Gotham's new mayor. Her assassination was thwarted by both Batman and Catwoman, who defeated Riddler's army and put an end his schemes for good - through there were still a healthy number of Riddler victims even without Bella Reál being added to the list of people Edward Nashton killed in The Batman.