The far-field super-resolution focusing devices possess characteristics such as super-resolution focusing, achromatic, small size and easy machining, which make them highly promising in optical imaging, optical microscopy and lithography. In this work, we propose a binary-amplitude modulation-based method for generating far-field super-resolution achromatic focusing. By using the principles of optical super-oscillation, combined with angular spectral diffraction theory and binary particle swarm optimization (BPSO), we optimize the binary amplitude-type far-field super-resolution focusing devices, which have an identical radius of 100λ but different focal lengths: λ₁ = 405 nm, λ₂ = 532 nm and λ₃ = 632.8 nm, respectively. Additionally, an achromatic metalens is integrated by using Boolean AND operation. To assess the feasibility of our proposed approach, numerical simulations are conducted via COMSOL Multiphysics employing FEM analysis. The simulation results demonstrate that the generated spots are located at 25.105λ, 25.106λ, and 25.105λ, respectively. The corresponding full width at half maximum (FWHM) values are 0.441λ₁ (0.179 μm), 0.469λ₂ (0.249 μm) and 0.427λ₃ (0.270 μm), which are smaller than the Abbe diffraction limit, and the far-field super-resolution achromatic focusing is realized. The sidelobe ratios are at low levels, i.e. 12.5%, 12.6%, and 14.2%. The binary amplitude-type far-field super-resolution achromatic devices have the advantages of easy machining, achromatism and super-resolution, and are suitable for miniaturization and integration of optical systems.