From the Super Mario Wiki
In The Super Mario Bros. Super Show! episode "20,000 Koopas Under the Sea", Captain Abidab appeared in the middle of a rally being held by King Koopa, who claimed he could get rid of a sea monster that was terrorizing Happy Harbor. Appearing after King Koopa had sarcastically asked Mario and Princess Toadstool, who had revealed King Koopa to be evil, how they would get rid of the sea monster , Captain Abidab claimed that she could get rid of the sea monster, which King Koopa scoffed at before leaving with his two Bloober minions, Captain Abidab, after everyone else ran away, recruited Mario, Luigi, Toad and Princess Toadstool as her crew.
Later, Captain Abidab introduced Mario, Luigi, Toad and Princess Toadstool to her ship, the Peapod. Captain Abidab began to show doubt at Mario, Luigi and Toad's effectiveness as her crew, as the three of them proved highly incompetent as sailors; Captain Abidab was reassured of Mario, Luigi and Toad's effectiveness by Princess Toadstool, who showed some doubt at her own words.
When the search for the sea monster proved fruitless after a while, Captain Abidab decided to expand the search for it and go underwater, much to Luigi's chagrin. After putting on a diving helmet and giving Mario a plunger-loaded harpoon gun, Captain Abidab dived underwater, with Mario, Luigi, Toad and Princess Toadstool following her. While walking on the ocean floor, Captain Abidab, Mario, Luigi, Toad and Princess Toadstool were ambushed by the sea monster, which Mario managed to hit with a plunger launched from his harpoon gun. Grabbing on to the rope dangling from this plunger, Mario, Luigi and Princess Toadstool were pulled by the sea monster for a brief amount of time, before being devoured by it, much to Toad and Captain Abidab's horror. When the sea monster began to approach them, Captain Abidab and Toad managed to escape it's sight by hiding in an underwater pit; after the sea monster passed by them, Captain Abidab and Toad followed it to the surface, where they saw it bash into the Peapod before submerging underwater.
Later, as Toad bailed water from the Peapod, which Captain Abidab steered, he saw a message in a bottle, which he reeled in and gave to Captain Abidab. Reading this note, Captain Abidab told Toad that it was from Mario, who claimed Koopa Nemo was going to attack Happy Harbor with a submarine. After reading this note, Captain Abidab set sail for a shortcut to Happy Harbor. By the time Toad and Captain Abidab reached Happy Harbor, Koopa Nemo had already begun to attack the ships there with his Koopilus submarine, which was the sea monster. Using a makeshift catapult, Captain Abidab managed to launch Toad into the Koopilus's mouth, hoping that Toad could find Mario, Luigi and Princess Toadstool in the giant submarine.
After the Koopilus was destroyed and Koopa Nemo was defeated, Captain Abidab was among the people who cheered for Mario and Luigi for them having saved Happy Harbor.