The Duckmobile was the main form of amphibious transport used by The Penguin. It was housed inside his sewer lair. It is based on a similair vehicle used by the villain in the contemporary film Batman Returns.
The Duck is first seen when The Penguin rewards Arnold Rundle with a $400,000 check. He then boards Rundle into the Duck that vanishes down into a raging whirlpool. It was subsequently seen when Pierce Chapman follows The Penguin's ransom instructions, he fell into the sewers where the Duckmobile was waiting for him. The Duck took Chapman to the opera house where he handed the money to The Penguin for Veronica Vreeland's release.