Sephiroth was raised from birth to be a super-soldier. He was injected with cells from Jenova, an extraplanar entity with vast power, as well as mako energy, a form of energy that produced magic but that had teratogenic powers in large amounts.
In short, Sephiroth was both raised from birth and biologically programmed to be that powerful.
Let's not forget he's also a SOLDIER 1st Class.
and later he merges/absorbs jenova