Young Female Volunteer: You're the coolest role-model a young person could have!
The Penguin: And you're the hottest young person a role-model could have.
The Penguin: Just relax. I'll take care of the squealing, wretched, pinhead puppets of Gotham!
The Penguin: I am not a human being, I am an animal!
The Penguin: You're just jealous because I'm a genuine freak and you have to wear a mask.
Henchman: Penguin... Killing sleeping children. Isn't it that a little ah...
[Penguin grabs an umbrella and shoots Henchman dead.]
The Penguin: No! It's a lot!
The Penguin: It's true I was their number one son... But they treated me like number two!
Catwoman: I am Catwoman. Hear me roar.
Answer: Nothing was stopping them. After Penguin's true nature was revealed, they most likely started searching the entire sewer system but couldn't find where his lair actually was so they had no choice but to give up.