In case of Be electron has to be removed from an s-orbital whereas in Boron removal takes from p-orbital.
As s-orbital is closer to nucleus, hence removal of electron is difficult which raises its ionization enthalpy.
Comparing O and N, nitrogen has completely half filled p-orbitals, hence I.E. of nitrogen is greater than oxygen. [Half filled orbitals account for greater stability].
Comparing O and F, F has increased nuclear charge and small size, hence removal of electron is difficult. Therefore, I.E. F is greater than O.