Alchornea cordifolia (Schumach. & Thonn.) Müll. Arg. is a well-known African medicinal plant traditionally used for various healing purposes. In the present study, methanolic, ethyl acetate and infusion extracts of A. cordifolia leaves were studied for their total phenolic and flavonoid contents and screened for their chemical composition. Moreover, the enzyme (acetyl- and butyryl-cholinesterases, α-amylase, α-glucosidase, and tyrosinase) inhibitory and cytotoxicity activities on HepG2: human hepatocellular carcinoma cells, B16 4A5: murine melanoma cells, and S17: murine bone marrow (normal) cells of extracts were evaluated. Finally, components-targets and docking analyzes were conducted with the aim to unravel the putative mechanisms underlying the observed bio-pharmacological effects. Interestingly, the infusion and methanolic extracts showed significantly higher total phenolic and flavonoid contents compared with the ethyl acetate extract (TPC: 120.38–213.12 mg GAE/g and TFC: 9.66–57.18 mg RE/g). Besides, the methanolic extracts followed by the infusion extracts were revealed to contain a higher number of compounds (84 and 74 compounds, respectively), while only 64 compounds were observed for the ethyl acetate extract. Gallic acid, ellagic acid, shikimic acid, rutin, quercetin, myricetin, vitexin, quercitrin, kaempferol, and naringenin were among the compounds that were commonly identified in all the studied extracts. Additionally, the methanolic and infusion extracts displayed higher antioxidant capacity than ethyl acetate extract in all assays performed. In ABTS and DPPH radical scavenging assays, the methanol extract (500.38 mg TE/g for DPPH and 900.64 mg TE/g for ABTS) exhibited the best ability, followed by the water and ethyl acetate extracts. Furthermore, the extracts exhibited differential enzyme inhibitory profiles. In particular, the methanolic and infusion extracts showed better cytotoxic selectivity activity against human hepatocellular carcinoma cells. Overall, this study demonstrated A cordifolia to be a species worthy of further investigations, given its richness in bioactive phytochemicals and wide potentialities for antioxidants and pharmacological agents.