Rapid global urbanization has precipitated a profound mental health crisis in high-density megacities, necessitating the urgent exploration of nature-based public health interventions. This comprehensive study investigates the critical role of urban green spaces in ameliorating psychological distress and enhancing cognitive function among adult populations residing in hyper-dense urban environments. Employing a rigorous sequential explanatory mixed-methods research design within the densely populated context of Dhaka, Bangladesh, the study correlates objective geographic measures of green space accessibility and vegetation density with self-reported mental health outcomes and standardized cognitive performance metrics. The quantitative findings indicate a robust, statistically significant inverse relationship between residential proximity to high-quality green infrastructure and the prevalence of generalized anxiety and chronic depression, alongside notable improvements in directed attention and working memory capacities. The qualitative analysis deeply elucidates the underlying psychosocial mechanisms driving these benefits, highlighting attention restoration, stress recovery, and enhanced social cohesion as the primary mediators of psychological well-being. Ultimately, this research convincingly argues that equitable, widespread access to high-quality urban green spaces must be prioritized not merely as a superficial aesthetic amenity, but as a fundamental, non-negotiable pillar of preventative mental health care and sustainable urban planning in the twenty-first century.