In a somewhat run-down suburb of Gotham City, a window of a house opens, seemingly of its own accord, and then a disembodied voice wakes the young girl sleeping in her bedroom, Kimmy. She wakes up and greets her friend, "Mojo." To her delight, invisible hands place a gold locket around her neck, and Mojo promises to bring a pearl necklace when he next visits. Kimmy mentions that she and her mother are planning to move away soon, and there is shock in Mojo's voice. Then Kimmy's mother, Helen, comes in, asking who Kimmy was talking to. Kimmy says, Mojo, and Helen chuckles, thinking her daughter has an imaginary friend.
The next day, a man, Lloyd Ventrix, enters the men's room at a jewelry expo, and covers himself in a sheath of grey material, then touches a button on his watch, and becomes invisible. He then walks outside and proceeds to lift jewels off their displays in plain sight, as people stare, baffled. Bruce Wayne happens to be attending the expo, and after a quick costume change, takes off after the invisible man. He corners the ghost at a construction site, and reveals him by throwing a can of paint. However, the man just touches his watch again, and the paint burns away, making him invisible again. He taunts Batman, who is unable to follow his voice because of the echoes caused by the narrow walls of the site, then gives him a sound beating, before slipping away. Back at his hideout, Ventrix becomes visible again, then empties out his loot. Looking at a photo of Kimmy, he says bitterly that Helen is trying to take her "where [her] dear old Dad can't find [her]." He vows that he won't let her.
Helen drops Kimmy off at school, and then goes to her job as a cashier at a grocery store. On her lunch break, she is confronted by Ventrix, her ex-husband, dressed in a smart suit and offering to pay for her lunch. He swears that he's not only turned over a new leaf, but is doing very well, and can provide Helen and Kimmy with everything they need. Helen refuses to have anything to do with him, and ignores his pleas to at least be allowed to see Kimmy.
Bruce remembers the name of a scientist, Dr. Karos, who approached Wayne Tech with a project, a "Cloak of Invisibility." Lucius Fox remembers that they were interested, but Karos suddenly withdrew his proposal. Karos passed away a year ago, but his assistant, Sam Giddell, is still alive.
Suspecting that Giddell might be the invisible man, Batman enters Karos's old lab and confronts him. Giddell swears that he was working in the lab at the time of the robbery. Seeing a roll of the special plastic Karos invented, Batman asks how it works. Giddell explains that when an electrical current is run through the plastic, it bends light instead of absorbing it – but the electricity also makes the plastic toxic, which is why Karos withdrew his proposal. Giddell has been trying to correct the problem, but without success, and so he is preparing to destroy all of the plastic. But he has noticed that some of it seems to be missing; when asked who else might know about the plastic, Giddell remembers the "errand boy" who worked in the office, an ex-convict: Ventrix.
That night, Batman tracks down Helen outside her house, to tell her about the plastic. Unknown to either of them, inside "Mojo" is giving Kimmy the pearl necklace he promised her, and then leads her by the hand out of her window, to show her a "surprise."
Realizing the truth behind Kimmy's "imaginary friend," Helen rushes back inside and sees her daughter gone. Since she has only been gone a few minutes, Batman takes off after them. In an abandoned drive-in theater, "Mojo" reveals his face, telling Kimmy who he really is. Kimmy recoils, since her mother has always told her her father is a "bad man." Ventrix tries to drag her into the car, when Batman catches up with them. Ventrix lets her go, and Kimmy runs back home.
Ventrix gets into his car, which he has also sheathed in the plastic, and turns it invisible, before driving straight at Batman. Batman manages to jump onto the roof of the car, which crashes after a wild chase. After driving off a set of elevated train tracks, the two men end up on a roof beneath a water tower. Batman takes a beating from Ventrix, who is still invisible, and refuses to listen as Batman tries to warn him about the suit's toxicity. Finally, Batman throws a trio of Bat Stars into the water tower, causing a shower of water that reveals Ventrix, and Batman quickly subdues him.
On a later night, Kimmy is talking to someone outside her window, saying that she and Helen will be moving away to where Ventrix can't find them. Helen rushes in, alarmed, and asks who she is talking to. Kimmy says, Batman. Helen, who has been hearing Kimmy talk to Batman a lot lately, doesn't believe her – not knowing that this time at least, Batman is indeed on the roof of their house. 
