Addressing the slow convergence, imprecision, and local optima pitfalls of traditional metaheuristic algorithms, this study innovatively proposes the hyper-chaotic nonlinear artificial hummingbird algorithm (HCNAHA), which integrates a discrete hyper-chaotic system into the foundational framework of the conventional artificial hummingbird algorithm. A sine-arccosine symmetrically coupled hyper-chaotic system (SCSC) has been constructed and is characterized by exceptional spatial ergodicity, rapid trajectory divergence, and high sensitivity to initial values. Utilizing the chaotic sequences generated by SCSC, a chaotic domain traversal flight strategy is devised, harmoniously integrated with the natural foraging behaviors of hummingbirds—such as guided-foraging, territorial-foraging, and migratory-foraging—to broaden the search for potential optima, enriching the behavioral diversity of algorithm agents and promoting balanced exploration and exploitation, thereby mitigating premature convergence. Comparative experiments with 11 other metaheuristic algorithms on the CEC2019 and CEC2022 benchmark suites, alongside fitness curves, box diagrams, and Friedman test results, demonstrate HCNAHA's superior optimization performance, robustness, and precision, showcasing its vast potential for future applications.