Papageno is singing his song Der Vogelfänger bin ich ja ("The Birdcatcher I Am") from Mozart's opera "The Magic Flute". The specific verses you can read here can be roughly translated as follows:
"The bird catcher I am, always jolly heißa hoppsassa!"
and
"I want a net for girls, I would catch them for me in the dozens!"
The comedy (with guys following Chupacabra behind and all). The lyrics, I didn't understand very well because I don't know German (that's a pity, because it's a beautiful language. The only thing I know about this language is Rammstein lyrics XD)
(Forsooth, and old unanswered comment!? It shall be so no more!)
It's quite slapstick-like, which sometimes can be tricky to convey in comic form!
It's behavior does seem closer to a cat (does whatever it wants!) than a dog...