Inque's origins and background remain largely undisclosed, but it is known that she was born into extreme poverty. Her precarious lifestyle eventually instilled in her an obsession with money, which ultimately became her raison d'être. She decided to take the easy way out and turned to the life of crime.
Early in her youth, she had a daughter, Deanna Clay. The identity of her child's father is not known nor are the circumstances of the child's birth. Because she was being chased by the police, Inque was compelled to remand Deanna to the care of unnamed guardians.
At some point after that, she allowed herself to become a biogenic mutant, allegedly for a substantial amount of money. The details of the experiment, who conducted it or if creating a shape shifter was the true goal remain undisclosed. From that point on, Inque put her talents up for hire and became a corporate saboteur and assassin for very large fees. Her activities before clashing with Batman are unknown, but by then she had become one of Interpol's most wanted. Even though she never returned to reclaim her daughter, she continually provided her with money, which she transferred to her trust fund on a monthly basis.
One such assignment saw Derek Powers commission Inque's services to sabotage Foxteca. On the first night, she crept into one of Foxteca's buildings and short-circuited a control panel causing a few floors to explode. On the next morning, she was disguised as a sculpture in Powers' office, and overheard Bruce Wayne's accusatory warning to Powers. She feared he might be onto something, but Powers quickly dismissed her concerns and gave her another assignment.
On that night, she broke in another Foxteca facility and spread havoc from within. However, this time she was interrupted by Batman, who had been sent by Bruce to look out for the company. Inside, Inque caught Batman by surprise and thrashed him around before fleeing through the ventilation conduct.
Later on, Inque resumed her task and sabotaged a Foxteca harbor. However, this time she was mildly foiled by Batman. Once again she engaged him, but this time he was prepared. Still, Inque was considerably superior in strength and dexterity, managing to repel every of Batman's attacks — she even mocked him, claiming he was not a fast learner. She attempted to flee, but she was surrounded by water, which made escaping more difficult. Batman quickly caught on to her vulnerability and Inque was forced to tear the ground apart, causing Batman to fall down the dam.
On the next morning, Inque reported back to Derek Powers and witnessed his delicate condition once he ascertained that Batman had been running interferences. She also told him he had an accomplice, because she heard him talking to someone over a comlink. Powers then told her to kill them both for all the money she wanted. Inque was delighted and remarked how much she enjoyed working for him.
Inque once again wrecked a Foxteca building, but this time as a means to distract Batman while she snuck on to the surface of the Batmobile so she would be taken to the Batcave. There, the extra weight she laid on the Batmobile was detected by the Batcomputer. The detection was too late, however, and she tackled Batman before he could defend himself. Inque wasted no time and attempted to suffocate Batman by pouring herself down his throat. She would have been successful, had Bruce not doused her with water.
She quickly recovered and cut off the end of the fire hose. She then headed upstairs, but was blocked by metal door, which when she tired to get through, released an electric charge. Relentlessly, she tried to bring the ceiling down and then attempted to squash both Batmen with the giant penny. Terry was under her grasp, but he quickly shocked her with another discharge. Aggravated, Inque trashed a few rogue's displays. When she lunged at Terry, he used Mr. Freeze's gun to immobilize her. Inque broke down into pieces of ice, which were then delivered to Police Commissioner Barbara Gordon in a giant bag.
Subsequently, Inque was transferred into Gotham Cryogenics, where she was held captive in a block of ice and supervised by Aaron Herbst. Despite being immobilized, she retained consciousness, and as a result, she could see and hear her curator's incessant nattering and moaning about his pitiful life and his love for her. After being fired for inappropriate conduct, Aaron cut off the power source to Inque's cryogenic prison out of spite for his employers. Inque broke free, and quickly took over the entire facility, holding its employees hostage. She tried to sneak out in the shape of a trench coat, but was made out and intercepted by Batman. Inque seized a moment of mayhem to lunge at the freeze gun and break it. However, she was still outnumbered by the GPD, so she fled through the storm drain system.
Apparently, Inque's frozen state had damaged her DNA, and as a result she lost the capacity to revert to her human form. So, Inque turned to Aaron, and exploited his infatuation with her to enlist his help. They broke into Fulton Labs and gathered all the necessary components to restore her. Moments before leaving, Inque was assailed by Batman, and the ensuing battle shattered most of the laboratory. She attempted to smother Batman in her bosom, but he broke free. Inque was then ensnared in a special electrical batarang, but was rescued by Aaron, who surreptitiously overpowered Batman. Inque decided then to take up her old assignment — killing Batman. But before doing so, she wanted to draw out his collaborator — Bruce.
She took Batman to the old Gotham Hills Arena, and there she brewed a concoction that repaired her deficiency. After seeing Terry talk to Bruce over his comlink, she pulled him in close so her invitation could be heard back at the cave. She threatened to kill Terry if he didn't show and kissed Terry to stop him from telling Bruce not to come. When the time came for Aaron to claim his promised award, Inque injected him with half of the treatment that would give him the shapeshifting powers he so craved, turning him into a liquidated being.
When Bruce came to Terry's rescue, Inque ensnared him and tried to squeeze him. However, Bruce had secretly donned an exosuit before the battle and the two fought. Despite initially being taken off guard, due to the surprise appearance of the exosuit and the sheer strength it offered the elderly Wayne, she still managed to damage the armor, and had the advantage until she was interrupted by Aaron, who sought revenge for her betrayal. The fight gave Batman the chance to break free of his shackles and smash a skylight, allowing the rain to fall on her, diluting her into the sewers, despite her desperate attempt to reach the stabilizing chemical.
Inque looked like a regular human, except for her tones of blue. Whenever she went undercover, she assumed a featureless form, with a white oval on her face, making her unrecognizable.
Inque was a polymorph, able to change her size and shape at will. Her body was a thick dark fluid that she could shape into a wide variety of forms, and harden herself to create weapons. She could form tentacles, flatten herself into a puddle, and regenerate herself, even from some residue. She had super strength and the ability to climb up walls and ceilings. Inque also possessed telescopic vision.
Inque's liquid body was subject to dilution in water, and solvents had an adverse effect on her physiology. She would lose the ability to change shape if frozen