Why wave nature of light fails to satisfy photoelectric effect....? 

In case of a wave the energy is represented by the amplitude of the wave. So, considering light to be strictly of wave nature, a high intense beam of light of lower frequency should have enough energy to knock electrons away from their molecular orbits. But this is not observed practically.

Practically, photoelectric effect is observed for light of certain frequency only. If the frequency of light is below the threshold frequency then no photoelectric effect is shown whatever the intensity of the light is. This indicates energy from light is absorbed by the electrons in quanta.

This results in the failure of the wave theory of light to explain photoelectric effect.