Why does an accelerated charge radiate away energy?

It emits light, because it "stirs up" the electromagnetic field. To understand this, just dip your finger into a still pond and move it in a circle. Water waves will emanate from your finger. These waves have energy, which means energy is being taken away from you. Same goes for the charges.

In fact, this follows almost automatically from the finite propagation speed of light. The electric field of a stationary charge obeys Coulomb's law. If the charge suddenly starts moving, the field won't obey Coulomb's law anymore, but it can't instantly change everywhere because of the finite propagation speed. Instead a "shockwave" of information goes out from the charge at speed $c$. This shockwave contains electromagnetic energy and travels at the speed of light -- it is light.

An accelerating charge radiates energy because, according to Maxwell's equations, it produces an electromagnetic wave.

what type of energy would it radiate when accelerated and why?

In addition to kinetic energy, the electron-nucleus system also has energy stored in the electric field between the electron and the positively charged nucleus.