<p>Analyzing gyrotactic microorganisms offers valuable insights into the behavior of phytoplankton and other oceanic microorganisms. Gaining a deeper understanding of how these creatures react to ocean currents and variations in nutrient levels is essential for constructing accurate models of marine ecosystems and forecasting their reactions to climate fluctuations. Within the realm of aquaculture, gyrotactic microorganisms have potential as live feed for fish and various aquatic organisms. Their capacity to actively move through water makes them a more nutritious and enticing food choice when contrasted with static or non-motile feeding alternatives. The central aim of this investigation is to scrutinize the behavior of a shear-thinning non-Newtonian fluid (tangent hyperbolic) as it traverses stretchable surface. This analysis encompasses the consideration of influential factors, including variable viscosity, thermal radiation, mixed convection and activation energy. To establish a foundation for this examination, we employ a transformation approach, leading to the derivation of non-linear ordinary differential equations rooted in fundamental principles of mass, linear momentum, and energy conservation. To solve these governing equations, we apply the shooting technique to obtain numerical solutions. The study delves extensively into the attributes of various parameters used in the modeling process, such as the variable viscosity parameter, radiation parameter, mixed convection parameter, variable conductivity, Williamson parameter, and diffusivity. These parameter characteristics are comprehensively explored and visualized through graphical representations.</p>