Claw Island was the Riddler's island fortress and corporate headquarters for his NygmaTech company. The revolving tower absorbed all brainwave signals coming from Gothamites hooked on the NygmaTech Box.
After he successfully gained production capital of NygmaTech with the help of Two-Face, Edward Nygma was able to place his invention, The Remote Encephalogram Stimulator Box, in all electronic stores all over Gotham, and promised the buyers that it would "bring the joy of TV entertainment into their living rooms."
However, unknown to them, it was also removed their brainwaves while they were mesmerized by their 3D TVs and flew across the sky to Nygma's main base of operations called his "Little Black Box" on Claw Island where they were placed in his control room by a large green antenna and was then placed directly into his own brain while he sat on his throne with statues of "The Thinker" as armrests.
After he tricked his former employer, Bruce Wayne, into stepping into his new improved box that mapped the human mind, The Riddler drained his brain and stored that information in a tube shaped memory stick. Riddler played it back at his base into one of the armrests of his throne. He watched it with Two-Face, and, as they stared at one of the many screens in the control room, they saw an image of a bat that stated that Bruce Wayne was Batman.
Afterwards, they came up with a plan to defeat the Dark Knight once and for all.
Riddler and Two-Face broke into Wayne Manor with the plan of "Seize and Capture." While Two-Face and his henchmen took care of Bruce, Riddler found the location of the Batcave and blew most of its surroundings up with his Batbombs.
The two villains captured Bruce's girlfriend, Dr. Chase Meridian and left behind a riddle so that Batman would track them back to Claw Island. Chase was in shackles on Riddler's couch and was unable to move, but stated that Batman would come for her.
Riddler laughed and replied that he was counting on it. A projection in the sky of a huge question mark that appeared over the light of the Batsignal which indicated that Riddler had wanted Batman to find him and Two-Face.
After he solved the riddle along with various others that Riddler had sent him, Batman and his new partner, Robin, went on their way to NygmaTech. Riddler and Two-Face played "Battleship" which activated hidden bombs that were concealed in the sea around the island. One of them destroyed the Batboat, and forced Robin to eject.
Meanwhile, Riddler fired a burst of energy from the tip of his box, and caused the Batwing to plummet into the sea. While they were under the sea, Riddler's Frogmen attacked the Dynamic Duo, but Batman trapped them in a net and swam over to the Little Black Box. After he saw them on their way to the box, Riddler rubbed his hands in glee and said that the real game began. After they reached the island, the Dynamic Duo got separated by Robin being pulled with the island itself moving and Batman finding a door to get into the inside of the lair. As soon as Batman entered, the door sealed behind him.
Batman looked up to see a projection of question marks and began to climb the question mark shaped crags that led all the way up to the top.
Robin, meanwhile, had a fierce battle with Two-Face and literally nearly knocked him over the edge of the island. But Robin found that he couldn't kill Two-Face and helped him up. However, the crazed villain returned that gesture by holding him at gunpoint and took him inside the base where he was tied up, gagged, and placed in a glass cylinder along with Chase.
Batman continued to scale the wall. He saw a platform that was covered with sharp knives that were lowered on top of him. Thinking quickly, he cut through the chain that held it and used the broken part to go straight up to the top while the platform crashed to the spiky ground below. The Dark Knight finally reached the main control room where Riddler and Two-Face were waiting. Riddler revealed that he knew who Batman was and that his mind was the greatest riddle of all: "Can Bruce Wayne and Batman ever truly co-exist?"
With help of Two-Face's henchwomen: Sugar and Spice, they both pulled down two curtains to reveal the cylinders that contained Chase and Robin. Two hatches that lead to the spike covered pit opened below them. Riddler told Batman that with a single touch of the button on his skull cane, they would fall to their deaths and that he did not have enough time to save them both.
Just as Riddler was about to press the button, Batman decided to distract the Prince of Puzzlers with a riddle of his own. Unable to resist, Riddler took his hand off the cane, sat down on his throne, and listened eagerly. Batman gave his Riddle: "I see without seeing. To me, darkness is as clear as daylight. What am I?" Riddler scoffed and gave him the answer: "Please! You're as blind as a Bat!" That gave Batman the time that he needed to hurl a high energy charged Batarang at the main antenna of the Box.
The antenna shattered and caused a chain reaction that caused the whole base to explode. Two-Face, Sugar, and Spice fled for their lives while Riddler stared around in horror at his lair being destroyed and a massive overload of brainwaves fell on him which nearly split his skull apart and weakened him. Before he collapsed, Riddler pressed the button on his cane which caused the bottoms of the cylinders to open and dropped Chase and Robin to the pit below.
Batman dove after them, and used his bat grapples that attached to the girders, which saved both Chase and Robin.
While Batman and Robin were safely on the main girders and untied Chase, Two-Face appeared and proceeded to shoot them all. Batman tricked Two-Face into deciding with his coin, and, while he tossed it, threw a handful of identical decoys that caused him to lose his balance and fall to his death.
Batman returned to Riddler's control room which was now pitch black with a few burned out flashing lights and completely destroyed.
Riddler's mind was badly enfeebled by the brainwaves and he was badly injured by the explosion. He muttered to himself: "Why? Why can't I kill you? Too many questions. Too many questions."
Batman answered Riddler's riddle by saying that he had to save them both because he was both Bruce Wayne and Batman, not because he had to be, but because he chose to be.
As Batman went towards him, Riddler screamed because he saw a huge terrifying bat that came straight toward him. He was then taken to Arkham Asylum, for the criminally insane and was locked up.