Darla is the niece of Philip Sherman, a dentist. She is not antagonistic through evil or malicious intent but rather through rambunctiousness and the overexcitement of having pet fish, which ironically has frequently resulted in her killing them by accident.
Gill and the other fishes in Sherman's fish tank describe Darla as a fish killer and that Nemo is supposed to be her new pet fish. The last fish she received, Chuckles, was killed by her because she wouldn't stop shaking the bag Chuckles was in. In the scene where Darla is about to take Nemo from her uncle, Nemo plays dead, but Darla thinks he is just sleeping and starts shaking the bag. Gill then fires himself out of the tank and lands in her hair, causing her to drop Nemo bursting his bag. After Gill catapults Nemo into the air, Darla tries to grab him, but he lands in the sink and is swallowed into the drain leading to the ocean. Darla then looks down the drain and screams, "FISHY!" The drain squirts water in her face as she breaks it. It is unknown what happens to Darla afterward.
Darla, in a way, is very similar to Sid Phillips, as they are both naughty human children who serve as antagonists towards the main character's races (toys and fish, respectively), although while Sid is a genuinely nasty child (in the first Toy Story) who relishes in his sick experiments, Darla appears to be much more innocent and seemingly did not mean Chuckles and Nemo any real harm, and apparently genuinely caring for Nemo (evidenced by her calling out to Nemo when he went down the drain).
During Darla's visit, the patients sitting in the waiting room who hear the commotion between Dr. Sherman, Darla, and Nigel are a young boy (reading an Incredibles comic) and his mother, a brunette-haired woman, and a balding man.
The music that plays when Darla appears at her uncle's office is the theme from Pyscho (1960).
Even though she is the main antagonist in the film, she is mostly seen in her picture rather than in person.
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Note: The Whale and Gerald are technically characters and locations, as scenes in the film are set both inside and outside their bodies (with Marlin and Dory being trapped inside both of their mouths at one point).