Why does beryllium lose two electrons when it’s orbitals are already full?
Electrons exist in the outer spaces of elements, away from the nucleus. Orbitals are mathematical descriptions of places in these outer spaces where electrons seem to be when they are there; they can be mathematically manipulated and reorganized but are a way to help you imagine what is really going on.

Manipulating the electrons is done experimentally, not mathematically. E.g., an element can be ionized and the energy required can be measured. Beryllium can suffer the loss of up to four electrons: the first requires 9.3 eV, the second requires 18.2 eV, the third requires 153.9 eV, and the fourth requires 217.7 eV. The energy required to remove the first two electrons is in the range of other metals that lose two electrons (Mg 7.6, 15.0; Ca 6.1, 11.9 eV). So Be can lose 2 electrons with a relatively small amount of energy (which will be supplied by something like empty orbitals and ionic or covalent bonding energy to other atoms). Losing those last two is a big jump and essentially doesn't happen in chemistry (it happens in physics and mathematics!).

The empty orbitals on Be are quite high in energy, i.e., if you stuck an electron into a p orbital on Be, it would be floating so far out from the nucleus that it would be looking for a better place. The idea of orbitals gives you a mental picture of what might happen - whether it really happens or not depends on whether that mathematical picture is true and is the most stable (lowest energy) condition available.

Completing shells or orbitals is a qualitative way of looking at the issue, but numerically, ionization potentials gives you the data you need to develop the picture, and the orbitals (as calculated for the hydrogen atom) are a reasonable way to begin.