I'm not an English teacher, but I am a native speaker. I hope I can explain this well.
The phrase "have just begun" means that something has just started and it is still happening (or it is on-going). For example, "We have just begun the class," means the class has just started and it's still going on.
The phrase "had just begun" implies that it is no longer happening -- something had started but now it is over. "We had just begun the class," implies that the class had started, but then something happened to stop it, so the class isn't happening at the moment we are speaking -- or that that the speaker is talking about a class that happened in the past and is recalling something that happened at the start of the class (which at the time of the discussion is over).
So when the singer says, "Life had just begun," he means that he felt like he had just started living his life, but then he went and threw it all away by shooting someone.
Hope that helps :)