This study addresses the critical need to enhance mixing quality and cost efficiency in electroosmotic micromixers, crucial for various applications, such as chemical synthesis, medical diagnostics, and biotechnology, utilizing the precision of microfluidic devices. The intricate dynamics of time-dependent electroosmotic vortices induced by microelectrodes are investigated, exploring the nonlinear physics principles driving mixing enhancement. Specifically, an examination is made of how nonlinear phenomena, such as convective flow instabilities, chaotic advection, and nonlinear interactions between fluid flow and channel geometry, contribute to observed improvements in mixing performance. Through comprehensive numerical simulations employing finite element-based solvers, the impact of relevant parameters, such as voltage amplitude (V0), frequency (f), Reynolds number (Re), and Debye parameter (k), on mixing performance is systematically analyzed. Findings reveal that optimizing these parameters, coupled with the strategic design of micromixers featuring offset inlets and outlets, leads to a remarkable mixing quality of 98.44%. Furthermore, a methodology is proposed for selecting the optimal micromixer configuration (MM1), balancing mixing quality, and cost efficiency. This study advances the understanding of electroosmotic micromixers and provides practical guidelines for optimizing microfluidic device performance in diverse applications.