If your angle of incidence is shallow enough, you can reflect almost anything. This is why gamma ray space observatories use grazing incidence mirrors to focus the incoming gamma rays. Similar designs are used at particle accelerators to harvest radiation for other use.

Now if you want something close to normal incidence, things become much more difficult and you need to use Bragg reflectors (i.e., multilayers of materials with alternating index of refraction that is tuned to the wavelength you want to reflect). These work as well (e.g., in semiconductor production machines), but you will be restricted to a narrow band of wavelengths and incidence angles, and you may be restricted by the available materials. Not every wavelength you want to reflect may have materials available that have the appropriate indices of refraction.