Q:

How effective is water purification by boiling?

Does boiling water kill all harmful bacteria, fungus etc from water, or it is just a myth and removes only few of microorganism?

A:

To be precise, boiling water would not remove all bacteria as there are certain extremophiles that thrive at higher temperatures.
However, boiling of water is known to get rid of harmful pathogens. Boiling of water is a method of pasteurization, which means killing those organisms that can cause harm to humans. 
Quoting from New York State - Department of Health >>

Boiling water kills or inactivates viruses, bacteria, protozoa and
  other pathogens by using heat to damage structural components and
  disrupt essential life processes (e.g. denature proteins). Boiling is
  not sterilization and is more accurately characterized as
  pasteurization.
Cooking food is also a form of pasteurization. For pasteurization to
  be effective, water or food must be heated to at least the
  pasteurization temperature for the organisms of concern and held at
  that temperature for a prescribed interval.

