The synthesis of a new nickel(II) coordination complex bearing acenaphthenequinone bis(thiosemicarbazone), [NiL], a N2S2 tetradentate bis-Schiff base ligand (H2L), under reflux and sonochemical conditions is reported. These new compounds (H2L and [NiL]) have been characterized by using various techniques such as FT-IR, 1H NMR, ESI-Mass spectrometry, UV–Vis, TGA, and elemental analysis. In addition, molecular structure of the ligand, (H2L)2.4DMSO.H2O, and complexes [NiL]3.2.5CH3OH.0·5H2O (1) and [NiL].CH3CN (2) have been determined by single crystal X-ray diffraction studies. The molecular structures of the nickel(II) complexes (1 and 2) revealed that they are structural isomers differing in their chelate ring arrangements (symmetric 5–5–5-trichelate system for 1 and asymmetric 4–6–5-trichelation for 2). In addition, the anticancer activity of H2L and its nickel(II) complex, [NiL], have been evaluated against human breast cancer cell line (MCF-7) using colorimetric 3-(4,5-dimethylthiazol-2yl)-2,5-diphenyl tetrazolium bromide (MTT) assay. The cytotoxicity of both compounds was compared with two standard anticancer drugs, cisplatin and oxaliplatin. Density functional theory (DFT) calculations were done to predict the chemical reactivity of H2L and complexes 1 and 2. Furthermore, DNA binding with H2L and [NiL] was performed using docking simulation to reveal that acenaphthenequinone and amine groups in thiosemicarbazone moieties in both ligand and complex are responsible for the groove binding to DNA via the formation of hydrogen, pi-anion, and pi-sigma bonds.