The development of optical systems operating in the far ultraviolet range (FUV, λ=100-200 nm) is limited by the efficiency of passivated aluminum (Al) mirrors. Although it is presently possible to obtain high-reflectivity FUV mirrors through physical vapor deposition, the process involves deposition with substrates at high temperatures, which is technically challenging for large optical elements. A novel passivation procedure for bare Al mirrors is reported. The treatment consisted of using a low-temperature electron-beam generated plasma produced in a gas mixture of Ar and SF₆ to etch away the native oxide layer from the Al film, while simultaneously promoting the generation of a thin aluminum tri-fluoride (AlF₃) layer on the Al surface. In the first section we analyze the effect of varying both ion energy and SF₆ concentration on the FUV reflectance, thickness, composition, and surface morphology of the resulting AlF₃ protective layers. In the second section, the reflectivity of samples is optimized at selected important FUV wavelengths for astronomical observations. Notably, samples attained state-of-the-art reflectances of 75% at 108.5 nm (He Lyman γ), 91% at 121.6 nm (H Lyman α), 90% at 130.4 nm (OI), and of 95% at 155.0 nm (C IV). The stability over time of these passivated mirrors is also investigated.