Jenna Duffy was a pickpocket and con artist operating out of Keystone City who moved to Gotham when she attracted unwanted police attention.
Eventually, she was enlisted by Tweedledum and Tweedledee to serve as the Carpenter for their new Wonderland Gang. The gang has been incarcerated by Batman at least twice, but she appears to continue to be an active member. She debuted in 2008.
The Detective Comics
Her first appearance is in Detective Comics #841, where Batman investigates a growing new team of costumed crooks, "The Wonderland Gang". Led by the Mad Hatter and featuring Tweedledum and Tweedledee, they quickly amass high-class muscle from all over Gotham dressed as different Lewis Carroll characters, such as the Walrus, the Carpenter, the Lion, the Unicorn, and the March Hare. Finding the crimes somewhat amiss, Batman eventually tracks the gang down to the House of Mirrors at the Gotham Amusement Park. He finds Tetch, the Mad Hatter, spinning aimlessly on the Teacups ride. Sure enough, Tetch is victim of one of his own mind-controlling chips, which Batman removes. He then goes in and confronts the gangs real leaders, Tweedledum and Tweedledee.
While Batman is battling the rest of the Wonderland gang, Tweedledum and Tweedledee both escape outside only to be subdued by the Mad Hatter, who beats them both unconscious with an oar. Batman calls Jim Gordon to tell him where to pick the gang up, and to make sure his men know to take it easy with Jervis Tetch, who really hadn't done anything wrong.
She makes an appearance with few of her new friends, the Walrus and the Tweeds, in Detective Comics #847, where they made another attempt to commit their crimes, but while Batman was busy going against Hush, Nightwing, Robin, Catwoman, and Zatanna apprehended the Wonderland Gang once again.
Gotham City Sirens
She makes three appearance in the Gotham City Siren comics. In Gotham City Sirens #5, she is requested by Catwoman, to help reconstruct the recently destroyed headquarters of Harley Quinn, Poison Ivy, and Catwoman's. In Gotham City Sirens #6, she gets more of her equipment from her van and continues to rebuild their hideout. She is called by Catwoman and Poison Ivy, who are in a life and death situation, and comes to the rescue to aid them. In Gotham City Sirens #7, she is finished with the repairs and demanded more money from Catwoman, since she did her job 'legally', which Catwoman agreed, due to Jenna saving her and Pam's lives.
Batman: Streets of Gotham
She made a recent appearance in Batman: Streets of Gotham comics. In Batman: Streets of Gotham #12, she is requested by a new villain that goes by the name of the Director. This business is handled by her partner, the Broker. She earns his respect when his bodyguards ambush her and she defeats them. Her job for the Director is to fill a stage full of death traps, and Batman will become the main actor, who will die on stage while the Director films it all. When she is done, she assumes that she can leave, but is quietly ambushed by goons and taken away.
In Batman: Streets of Gotham #13, she realizes that not only will Batman die on the stage, but she will be killed as well. She tries to escape, but is stopped by the Director and his goons. After awhile, she hints to Batman all of the traps she had set up for him on stage. The Director holds her at gunpoint, but she puts him in a pool filled with electric eels. She manages to escape with her life and Batman easily defeats the Director on his own stage. She tells Batman about her supposed abduction, her forced labor without pay, and that she was to be killed by the Director as well. Batman advised that she leave Gotham, but as she found work in Keystone again, the Broker called and persuaded her to come work for him with Mr. Freeze, with the pay in diamonds. She returns to Gotham at this point.
In Other Media
Although she doesn't appear in the game, the Carpenter makes several appearances in the Arkham City comics. In the 2nd digital issue, it is explained that Batman gave her the chance to escape incarceration via a bus ticket to Keystone City, albeit she leaves her equipment in Gotham. Taking up the offer, Duffy boards the bus, however it is later revealed that her former Wonderland gang tipped off Strange to her attempted escape, allowing TYGER guards to intercept the bus and take it to Arkham City itself.
Jenna is later seen in Arkham participating in Two-Face's trial against the Joker as a juror, where she voted him guilty. Later, Carpenter was kidnapped by Mad Hatter as one of the mind-controlled "Alices" at his tea party before being rescued by Batman during his investigation into Protocol 10.
It can be assumed that after Arkham City was shut down Duffy was transferred back to Blackgate.
While never appearing on screen, Carpenter did appear alongside March Harriet in the comic "Harley loves Joker" which along with being set in the DCAU was written by Paul Dini.