She was a college student who majored in physics. One day, while on a fishing trip with some friends, a pirate named Captain Filch attacked their boat. Though her friends were able to escape, Filch kidnapped Mona Lisa and tried to convince her to help him with his experiments on his submarine, so he could take over the world. Mona Lisa played along, and one night, she tried to destroy his nuclear reactor and was mutated in the process. After this, she vowed to stop Filch.
She and Raphael met in the episode 'Raphael Meets His Match', when Filch was holding a yacht full of people hostage and teamed together to stop him. Afterward, she followed the Turtles back to New York, but was never seen again.
Based on her interaction with Raphael and the episode's title, she was supposed to be his love interest. However, like Lotus Blossom (who had one more episode), we never see or hear about her after her appearance.
After her transformation, Mona Lisa had webbed fingers, could jump extremely high, and used her highly developed legs for attacking. She physically resembles a salamander, only with breasts and hair (distinctively mammalian traits). She also had a yellow torso on her body that resembled a leotard.
Before her mutation, she was a Caucasian female presumed to be in her late teens/early 20s with brown hair held back in a ponytail by a pink hairtie and had black eyes. She wore a pink dress with matching heels and gold bangles and necklaces. She was also seen wearing a lifejacket before her kidnapping.
The backing card for the Mona Lisa action figure identifies her as "The lovely lizard lady." Mona Lisa was slightly re-designed for the action figure; in the TV episode she had brown hair and two-toed feet, but her action figure version has black hair and three-toed feet.
Out of universe information
"The character of Mona Lisa was created for the old show by someone working for Fred Wolf. What many people do not know was that she was originally supposed to be a female mutant turtle, but Kevin and I put our foot down (this was back when we both agreed that a female turtle was a lame, stupid, creatively bankrupt idea) and they changed her to some kind of lizard." --PL
This would also explain why no animal was present for her mutation, as well as confirm her reptilian origins, including why she still had "turtle feet."