Planar super-oscillatory lens (SOL), a far-field subwavelength-focusing diffractive device, holds great potential for achieving sub-diffraction-limit imaging at multiple wavelengths. However, conventional SOL devices suffer from a numerical-aperture-related intrinsic tradeoff among the depth of focus (DoF), chromatic dispersion and focusing spot size. Here, we apply a multi-objective genetic algorithm (GA) optimization approach to design an apochromatic binary-phase SOL having a prolonged DoF, customized working distance (WD), minimized main-lobe size, and suppressed side-lobe intensity. Experimental implementation demonstrates simultaneous focusing of blue, green and red light beams into an optical needle of similar to 0.5 lambda in diameter and DOF > 10 lambda at WD = 428 mu m. By integrating this SOL device with a commercial fluorescence microscope, we perform, for the first time, three-dimensional super-resolution multicolor fluorescence imaging of the unseen fine structures of neurons. The present study provides not only a practical route to far-field multicolor super-resolution imaging but also a viable approach for constructing imaging systems avoiding complex sample positioning and unfavorable photobleaching.