Killing Barbalib is the 2nd episode of Barbapapa (1998 TV series).
The episode starts with Barbabright deciding it was a good day to build a bomb (he says this every day, but today was special because this was the first day Barbabright kept all of his limbs while building a bomb). Then, because he's bored, he throws the bomb at Barbalib. Barbalib survived, unfortunately.
At about the same time, Barbazoo decided Barbabravo hasn't had enough butt-kicking yet. To fix this, Barbazoo sneak up on Barbabravo, and shoots him with a shotgun. Barbazoo incurs the wrath of Barbabrabo. Barbazoo is smart enough to hide, so Barbabravo attacks Barbalib instead.
Barbamama is playing with the Teletubbies, when suddenly Barbalib comes in and dropkicks all of Barbamama's friends. Barbamama, furious that Barbalib didn't dropkick him too, attacks Barbalib. Barbalib is shredded by Barbamama's vicious claws, teeth, and gum. Barbalib doesn't survive, fortunately.
Then Barbalib decides he's sick of all this crap, and he jumps off of a cliff. Barbalib dies. But then the characters of My Little Pony: Friendship is Magic show up and do bad things to Barbalib's corpse.