Tiffany Ambrose was Roman Sionis' girlfriend. She was involved in various crimes, including drug trafficking. Tiffany was eventually murdered by The Joker after she was shot through the heart, who forced Sionis to commit the act.
Tiffany Ambrose had an extensive list of priors while she was Sionis' girlfriend, including drug trafficking. Days before Christmas Eve, Tiffany ended up spooked by a new psychopathic mass murdering criminal known only as the Joker. Sionis then had Tiffany go to one of his safehouses at Lacey Towers. However, the Joker had deduced Tiffany's location and stalked her. Tiffany then tried to text Sionis for help, only for the Joker to violently smash her head against a counter and knocked her unconscious. Joker then crucified her above a chandelier in the living room and lain in wait for Sionis and his body double: Giovanni Luchese. When Sionis tried to ambush Joker after he had killed Luchese, Joker managed to subdue him, and destroyed the room with a Molotov Cocktail. Tiffany's life was ended shortly thereafter when the Joker forced Sionis to fire his gun at Tiffany's heart, and, that the only other alternative was to have her die from smoke inhalation. Her body was later discovered by one of Sionis' rivals, The Penguin, which lead to him being implicated for the murder. Batman acted on a tip from the Penguin, analyzed the crime scene, and had managed to uncover the truth behind the murders, including that Sionis was still alive and was held hostage by the Joker so that the latter could rob the Gotham Merchant's Bank.
If the player listened in on the thugs at the Industiral District, they thought that Tiffany may have gotten Sionis hooked on drugs, as a possible explanation for his odd behavior (which was due to them not knowing that it's the Joker in disguise).
Although Tiffany did not actually appear in Arkham Origins Blackgate, she was alluded to in one of the casefiles, which mentioned that Black Mask, while he was incarcerated at Blackgate Prison, carried her photo with him constantly, which implied that he still loved her.