We report a novel s-tetrazine based covalent organic framework (TZA-COF) and its hybrid nanocomposites with reduced graphene oxide (TZA-COF-rGO) and Co metal to illustrate novel structure-activity relationships in this class of compounds for electrocatalytic oxygen reduction reaction (ORR). The Co-impregnated hybrid composites (TZA-COF-rGO-Co) were further annealed to yield Co-encapsulated nitrogen doped graphitic carbon (Co@NC-600), which exhibited excellent ORR activity comparable to that of the state-of-the art Pt/C in terms of onset potential, E1/2 (half-wave potential), 4e- reduction selectivity and methanol tolerance. Sequential mechanistic analyses of activity enhancement and electron transfer pathways for the ORR, at different stages of controlled catalyst engineering, elucidated the crucial role of active sites and overall catalyst nature in tuning the ORR mechanism. Co@NC-600 also exhibited high oxygen evolution reaction (OER) activity under alkaline conditions which makes it one of the most efficient non-precious metal bifunctional catalysts, capable of catalyzing complex 4e- reduction processes like the ORR and OER.