Two street artists, Daedalus Boch and Junkyard Long, break into Castle Hardware and start tagging the place. Batman arrives and takes them out, and then leaves them for the police. However, a white-clad figure steps into the hardware store and tells the two artists that he admires their destructive tendencies. He unties them and says that he wants to sponsor them as his patron, and gives them super-enhanced weapons. When Daedalus and Junkyard wonder who he is, the man introduces himself as Anarky.
At Wayne Manor, Tatsu works out in Bruce's workout room, dodging a series of mechanical traps. Alfred and Bruce are watching her on the monitors, and Alfred points out that Tatsu is almost as skilled as Bruce is. Unimpressed, Bruce says that he trained at dozens of dojos and each one required the completion of a different test. As they talk, the two men play chess and Bruce soon defeats Alfred. When Alfred wonders why Bruce bothers playing when he always wins, Bruce says that playing keeps him sharp, and tells his friend that it will take more than agility to convince him that Tatsu can function as his bodyguard.
Once Tatsu is done, she goes to her room and checks on a box in the closet. Inside the box is a glowing jade sword. Bruce calls her to the trophy room but when she gets there, there's no sign of Bruce. Tatsu notices a scuff mark on the fireplace mantle and, examining it, finds a hidden switch. The switch opens a door but there's a security palmprint scanner that doesn't recognize her.
Following directions from Anarky, Daedalus and Junkyard attack the Queen Street Gallery with their new weapons, an electric blaster and a chainsaw. Batman arrives, unaware that Anarky is watching the confrontation from hiding. The Caped Crusader takes on Daedalus while Junkyard leaps on the Batmobile and tries to cut it apart with an electric chainsaw. The chainsaw shatters on the armored exterior and Batman disposes of both artists.
Back at the Batcave, Alfred informs Batman that the newest attack is all over the news. They figure that the artists don't have the resources to buy the equipment they were using, meaning that someone is sponsoring them. Batman notices Junkyard's footprint on the Batmobile and has Alfred analyze the goo it left behind. When Bruce goes upstairs, Tatsu is waiting for him. She discusses her potential employment and asks him to keep an open mind. Bruce agrees and shakes her hand. Once he leaves, Tatsu removes the transparent film from her hand and studies it with satisfaction.
Daedalus and Junkyard are in a prison cell when Anarky cuts open the window. He informs them that as an agent of chaos, he fights against order and its representative, Batman. The villain then leads them to a nearby van and shows them a new stash of equipment, including power suits, and gives them to him.
Alfred runs a background check on the two artists and confirms that until they received their advanced weaponry, they hadn't committed any major crime. Bruce informs Alfred that the goo is a lubricant and contains traces of a pollen from the Chess Flower. Bruce figures that someone is manipulating Daedalus and Junkyard as part of some game against Batman. Bruce hacks the Gotham CCTV system and spots Daedalus and Junkyard, wearing their new costumes. Alfred wonders if Batman is going after them, and Bruce tells him to drive instead.
As Daedalus and Junkyard spread more graffiti, the Batmobile pulls up and fires on them. As the two artists fight back, they're unaware that Alfred is driving the Batmobile by remote control. He finally fires all of the weapons at once, sending them running for their rendezvous with Anarky.
At the Gotham Wheelhouse station, Anarky is monitoring his two pawns. Batman comes up behind him and Anarky hears him. The villain boasts that he's glad to have some opposition, and attacks his opponent.
Tatsu goes back to the fireplace and uses the copy of Bruce's palmprint to open the sealed door. There's an elevator on the other side and she uses to go down into what she discovers is a private library. Looking around, Tatsu finds one book marked with a section about the Gotham Wheelhouse.
Anarky proves a match for Batman and says that he's glad his opponent understands. The villain says that he doesn't care how much damage he does, but his ultimate goal is that as the white king, he represents anarchy. They fall onto the main wheel in the wheelhouse and one of the gondola struts explodes. Batman realizes that Anarky has planted bombs on the two gondolas, each one coming from opposite sides of the river. When they pass, the bombs will detonate simultaneously. Anarky boasts that there's only time for Batman to defuse one bomb. When Batman heads for the wheel control to stop the machinery, Anarky holds up a dead man's switch and warns that he'll detonate both bombs instantly if the hero doesn't play by his "rules."
Daedalus and Junkyard arrive in response to Anarky's summons, and he tells them to attack Batman and keep the hero distracted. Batman disposes of them for the third time and then heads for his Batcycle. He calls Alfred and has him send the tram schematics, and then blasts a hole in the side of the bridge. Batman then leaps the Batcycle out and uses his cape as a glider to soar to the top of the strut where the two gondolas will cross. Spotting the bombs, Batman realizes that they each have a magnetic trigger and will attract each other, setting them off. However, Anarky arrives and attacks him, threatening to trigger the bombs.
Furious that Batman isn't playing by the rules, Anarky complains that that Batman doesn't appreciate the honor of being chosen as his archnemesis. Batman tells him that he's making a logical choice to do something insane, and then attacks Anarky, knocking the dead man's switch out of the villain's hand. The bombs don't go off, and Batman explains that he used a frequency jammer to stop the detonation signal. He then hits Anarky, knocking him off the strut to fall to the bottom of the strut far below.
Racing against time, Batman swings down around the strut, letting his line wrap around the support. He then hooks the line up to a generator and feeds it power. The charge converts the entire strut into a magnet, overcoming the pull of the bomb triggers and neutralizing them. When Batman looks down again, he discovers that Anarky has disappeared.
As Lt. Gordon and his men take Daedalus and Junkyard away, Batman notices that Tatsu has arrived, having deciphered his clues. However, he wonders if she got lucky and drives off before she can spot him.