“The emperor penguin is technically a bird although one that makes his home in the sea. So if you're wondering what he's doing in Gotham City, well, that's part of our story.”
Where as most of Batman's enemies suffer from a major mental illnesses and have traumatic origins, Penguin really doesn't have either of those, so to sound more intimidating on the street and like he comes from old money he fabricated a fish story. Cobblepot claims he was taught English and mechanical engineering by a colony of hyper intelligent tropical penguins that escaped from the Gotham zoo. The penguins adopted him after he was thrown over a bridge by his wealthy parents when they found out their son had been born with freakish webbed hands and wouldn't present well playing the piano at parties. Killer Croc however has testified under oath that this tragic tale is a complete crock of shit, as any penguins would have been eaten by all the alligators living down there or by the orphan armies of the Sewer King. Aquaman was also called in as an expert character witness to confirm that none of Cobblepot's penguins were qualified to teach and couldn't earn as much as a fishing license.
Oswald's mother always made him carry an umbrella even on a sunny day and a tuxedo when it was hot because his father died of pneumonia, so naturally the kids at school made fun of him for the way he overdressed, how he waddled in gym class and for his penis like nose. Ostrichsized by his human peers Cobblepot had no one to play Monopoly with so he made feathered friends raising pigeons and racing them to help pay rent, while other boys his age were getting paper routes. Before long he branched out into cockfights down at the docks, where Cobbblepot became involved with Carmine Falcone's smuggling operations, where he used flocks of ducks and geese to sneak drug shipments past the police.
After a couple of gang wars, Penguin worked his way up the ladder of organized crime and now runs his own nightclub. These days he drinks like a fish, and smokes a pack of Kools cigarettes a day, with a chum bucket and caviar based diet rich in Omega 3 fatty acids. After an Elks lodge meeting, Cobblepot traded the water works and the boardwalk to Bruce Wayne for control of one of Gotham's four railways, hoping to spread the wings of his criminal enterprise. His plans were derailed by Batman however and he was incarcerated becoming the bird man of Black Gate penitentiary after it was determined he wasn't crazy enough to be shipped off to Arkham, although he easily would be after spending just a day in that hell hole of a hospital.
The Penguin thinks that he is a gentleman and dislikes getting his gloves dirty or his tuxedo stained in the blood of his enemies. The Penguin possesses a great deal of skill in aeronautical engineering designing jet packs for penguins and portable helicopter machine gun umbrellas. He refuses to sell these inventions to the air force or a commercial airliner and become a billionaire through legal means, due to all the birds sucked into jet engines each year.
The Penguin ran successfully for mayor in 2016, promising to curtail wind turbines and hydro electric plants for the sake of birds and fish everywhere, and to ensure the future of the clean coal and oil industries. The Penguin insisted global warming was nothing to worry about and ensured the voters that having Mr. Freeze shoot the ice caps with his freeze ray would offset the effects of increased carbon emissions on rising sea levels.
The penguin claimed to have won in a landslide victory, although the popular vote was clearly won by his opponent, Victor Szasz; the inauguration was followed by a catastrophic earthquake induced by fracking for oil in residential zones. His term in office was cut short however by the earth shattering, timeline resetting events of Oil Crisis.