The Birdosaurus is a pterodactyl-like beast with the sinister ability to show up randomly for the express purpose of screwing up Dr. McNinja's plans.
Dr. McNinja has sworn an oath to track it down and slay it. On Page 9 of the chapter "Paleontologists, Politicians, and Prologue", another Birdosaurus crashed through the ceiling of the oval office with a gun taped to one of its wing-claws with the apparent intent to assassinating president Funkhouser. At this point it was killed by Dr. McNinja, who had been relocated to the White House in his sleep and impaled the beast with his katana. Its corpse was then thrown in the trash, with the doctor at first believing that he had killed this nuisance of his endeavors, but then reasons that "That COULDN'T have been him. He's [his] greatest enemy... [It] shouldn't have been so easy."
The Birdosaurus finally met his demise is The End: Part 2, when, after King Radical killed Old McNinja and informed the doctor that this Birdosaurus was the one that had tormented him over the course of his adventures, and then proceeded to snap its neck in case Dr. McNinja had planned to personally kill it.