The key objective of this communication is to examine the significance of bioconvection in the magnetized flow of \({\text{Cu}} - {\text{Al}}_{2} {\text{O}}_{3} /{\text{H}}_{2} {\text{O}}\) hybrid nanofluid with gyrotactic microorganisms toward a curved oscillating surface. The organized macroscopic convective movement of fluid generated due to the presence of magnetic force, thermal radiation, chemical reaction, and density gradient produced by the swimming of microorganisms like algae and bacteria is termed bioconvection. The swimming of these self-propelled motile microorganisms in a certain direction enhances the density of the base fluid, thus producing bioconvection. The features of the first-order chemical reaction and thermal radiation are also invoked in the traditional concentration and energy equations, respectively. Nonlinear partial differential equations of the above-presumed flow problem are modeled via the curvilinear coordinate system. For a similar solution, the accomplished nonlinear partial differential equations are then transformed to dimensionless form with the assistance of similarity variables. The most efficient convergent technique, namely the homotopy analysis technique, is incorporated to obtain the solutions of the governing dimensionless nonlinear partial differential equations. The influences of various parameters on velocity, pressure, density of motile microorganisms, temperature, concentration, local Sherwood number, Nusselt number, and surface drag force are given in the form of tables and graphs and are discussed in detail. Graphical observations witness that the velocity amplitude diminishes with mixed convective variable, solid volume fraction parameter for copper, buoyancy fraction variable, and bioconvective Rayleigh number. It is also noticed that the magnitude of the Motile density number diminishes for developed values of the Peclet number, microorganisms difference constant and the bioconvective Lewis number, whereas its magnitude shows a favorable manner with the radius of curvature parameter.