Developing efficient catalysts for nitrogen fixation is becoming increasingly important but is still challenging due to the lack of robust design criteria for tackling the activity and selectivity problems, especially for electrochemical nitrogen reduction reaction (NRR). Herein, by means of large-scale density functional theory (DFT) computations, we reported a descriptor-based design principle to explore the large composition space of two-dimensional (2D) biatom catalysts (BACs), namely, metal dimers supported on 2D expanded phthalocyanine (M-2-Pc or MM'-Pc), toward the NRR at the acid conditions. We sampled both homonuclear (M-2-Pc) and heteronuclear (MM'-Pc) BACs and constructed the activity map of BACs by using N2H* adsorption energy as the activity descriptor, which reduces the number of promising catalyst candidates from over 900 to less than 100. This strategy allowed us to readily identify 3 homonuclear and 28 heteronuclear BACs, which could break the metal-based activity benchmark toward the efficient NRR. Particularly, using the free energy difference of H* and N2H* as a selectivity descriptor, we screened out five systems, including Ti2Pc, V-2-Pc, TiV-Pc, VCr-Pc, and VTa-Pc, which exhibit a strong capability of suppressing the competitive hydrogen evolution reaction (HER) with favorable limiting potential of -0.75, -0.39, -0.74, -0.85, and -0.47 V, respectively. This work not only broadens the possibility of discovering more efficient BACs toward N-2 fixation but also provides a feasible strategy for rational design of NRR electrocatalysts and helps pave the way to fast screening and design of efficient BACs for the NRR and other electrochemical reactions.