The ends do not justify the means. This might seem a naive concept to someone who has lost due to criminal action but think about it. Vigilantism is not a form of order, it is an act of anarchy. Society is based strictly on order and it is the very criminals who reject this order, the law, who promote anarchy. That is why vigilantes are no better than the criminals they kill.
Now if the vigilante were to apprehend criminals through non-lethal means or provide assistance to the police to apprehend them, then that would be okay. We also have the notion that we should remain vigilant to help defend against crime. In this idea all citizens have a duty, the responsibility to watch and report criminal actions to the authorities and to aid in police investigations.