Bored to death - Means "when someone is has absolutely nothing to do. He feels like he is going to die of boredom because of how bored they are
(Urban Dictionary - with some tinkering of mine.) Very or completely bored.
At the age of the singers, and coming from a young band, my educated guess is that what was meant was "searching boredom" (a boredom that is a search for action) Expressed by the opinion that the girl was "wasting her breath'' and "life is short" etc. He wants some action.
The kind when a young is at some club and then he says "aqui tá chato
, vamos pra outro lugar."
Types of boredom.http://news.nationalgeographic.com/news ... s-science/