The Claw Island is an island that was the Riddler's lair and a location in Batman Forever. It was where he absorbed all the neural energy (meaning memories and knowledge) of all of the citizens of Gotham City and it serves as the main base of operations for his company NygmaTech.
After successfully gaining production capital of NygmaTech with the help of Two-Face, Edward Nygma (now known as The Riddler) was able to place his latest invention, the Remote Encephalogram Stimulator Box, in all electronic stores all over Gotham City promising the buyers that it would "bring the joy of 3D TV entertainment into their living rooms."
However, unknown to them it was also removing their brainwaves while they were mesmerized by their 3D TVs and flying across the sky to Nygma's main base of operations which he called his "Little Black Box" on Claw Island where they were being placed in his control room by a large emerald-green crystal-like antenna and placed directly into his own brain while he sits on his throne with statues of "the Thinker" as arm rests.
After tricking his former employer Bruce Wayne into stepping into his new improved box that now mapped the human mind, The Riddler drained his brain and stored this information in a tube-shaped memory stick. He played it back at his base into one of the arm rests of his throne. He watches it with Two-Face and as they stare at one of the many screens in the control room, they see an image of a bat stating that Bruce Wayne was Batman.
Afterwards they began to come up with a plan to defeat the Dark Knight once and for all.
The Riddler and Two-Face broke into Wayne Manor with the plan of "Seize and Capture". While Two Face and his thugs were taking care of Bruce Wayne, the Riddler found the location of the Batcave and blew most of its surroundings up.
The two villains capture Bruce's girlfriend Dr. Chase Meridian and leave behind a riddle so that Batman will track them back to Claw Island. Chase is in shackles on the Riddler's couch and unable to move, but states that Batman will come for her.
The villain laughs and replies that he's counting on it. A projection in the sky of a huge question mark appears over the light of the Batsignal indicating that he wants Batman to find them.
After solving the riddle along with various others the villain had sent him, Batman and his new partner Robin are on their way to NygmaTech. They even passed through the altered version of the Batsignal and changed it back to normal. Riddler and Two-Face play "Battleship" which activates hidden bombs concealed in the sea around the island. One of them destroys Robin's boat forcing him to eject.
Meanwhile the Riddler fires a burst of energy from the tip of his Box causing the Batjet to plummet into the sea. While they are under the sea, frogmen attack the Dynamic Duo, but Batman traps them in a net and swim over to the shores of Claw Island. After seeing them on their way to the box, Riddler rubs his hands in glee saying that the real game begins. After reaching the island, the Dynamic Duo get separated by Robin being pulled with the island itself moving and Batman finding door to get into the inside of the lair. As soon as Batman enters, the door is sealed behind him. He looks up to see a projection of question marks and begins to climb the question mark shaped crags leading all the way up to the top.
Robin meanwhile has a fierce battle with Two-Face and literally nearly knocks him over the edge of the island. But he finds he can't kill him and helps him up. However the crazed villain returns this gesture by holding him at gunpoint and taking him inside the base where he is gagged, tied up and placed in a glass cylinder along with Chase.
Batman continues to scale the wall. He sees a platform covered with sharp knives lowering on top of him. Thinking quickly he cuts through the chain holding it and uses the broken part to go straight up to the top while the platform crashes to ground below. The Dark Knight finally reaches the main control room where the Riddler and Two-Face are waiting. Riddler reveals that he knows who he is and that his mind is the greatest riddle of all "Can Bruce Wayne and Batman ever truly co-exist?".
With help of Two-Face's henchwenches Sugar and Spice, they both pull down two curtains to reveal the cylinders containing Chase and Robin. Two hatches leading to the spike covered pit open below them. Riddler tells Batman that with a single touch of the button on his cane, they will fall to their deaths and that the Dark Knight does not have enough time to save them both.
Just as he is about to press the button, Batman distracts the Prince of Puzzles with a riddle of his own; unable to resist, the Riddler takes his hand off the cane and listens eagerly. Batman gives his Riddle: "I see without seeing. To me, darkness is as clear as daylight. What am I?" The Riddler scoffs and gives him the answer: "Please! You're as blind as a Bat!" This gives Batman the time he needs to hurl a high energy charge Batarang at the main antenna of the box.
The antenna shatters causing a chain reaction that causes the whole base to explode. Two-Face, Sugar and Spice flee for their lives while the Riddler stares round in horror at his lair being destroyed and a massive overload of brainwaves fall on him nearly splitting his skull apart and weakening him. Before he collapses, he presses the button on his cane which causes the bottom of the cylinders to open and drop Chase and Robin to the pit below.
Batman dives after them and by using bat grapples attached to the girders saves both Chase and Robin.
While they are safely on the main girders and untying Chase, Two-Face appears and proceeds to shoot them all. Batman tricks the villain into deciding with his coin and while he is tossing it, throws a handful of decoys causing Two-Face to lose his balance and fall to his death.
Batman returns to the Riddler's control room which is now pitch black except for one small flashing light and completely destroyed.
The Riddler's mind is badly enfeebled by the brainwaves and he is badly injured by the explosion. He mutters to himself: "Why can't I kill you? Too many Questions, Too many Questions."
Batman tells him that he had to save them both because he is both Bruce Wayne and Batman, not because he has to be, but because he chooses to be.
As the Dark Knight goes towards him, the villain screams because he sees a huge terrifying bat coming straight towards him. He is then taken to Arkham Asylum for the criminally insane.