It depends on the wavelength. If you choose a specific wavelength, a mirror can be designed to be as reflective as one can afford, for that wavelength, but it may be absorptive or transmissive to other wavelengths.
On the other hand, if you want a mirror that can reflect many wavelengths, metals are usually best for the visible range, but they all have some level of absorption, and reflection is not equal for all wavelengths.
As for most "impenetrable", again, this fundamentally depends on wavelength. See http://en.wikipedia.org/wiki/Attenuation_coefficient