Well, UV-C surely carries more energy than UV-A and UV-B, but the reason as to why UV-C radiation doesn't reach Earth is because of the presence of $O_2$ and $O_3$ in the stratosphere. UV-C radiation carries enough energy to excite an electron present in the oxygen molecule to shift to a higher energy orbital in the same oxygen molecule. Almost all energy from UV-C radiation is used up.
Now, this excited $O_2$ decomposes to form two free radicals of oxygen $[O]$ which further reacts with other oxygen molecules found in the atmosphere to create $O_3$ (Ozone) molecules.
In a way, the energy from UV-C is used up in creating $O_3$ molecules, therefore, there is no radiation reaching us. UV-A radiation, however, reaches us because $O_3$ is transparent to UV-A radiation, that is, UV-A radiation doesn't provide enough energy (wavelength is inversely proportional to energy) to excite the electrons present in $O_3$, so most of UV-A radiation reaches the Earth but certain UV-B radiations have the energy to excite electrons in $O_3$, therefore, not much of UV-B radiations reach the surface of the Earth.