Topology optimization under large deformation poses significant numerical challenges due to geometric nonlinearity and topology evolution. Material removal during optimization generates growing voids, which may lead to self-contact under large deformation. Moreover, the emergence of slender structural members makes buckling, snap-through, and snap-back behavior inevitable. Such nonlinear responses are difficult to capture using standard load- or displacement-controlled schemes, which often fail near limit points. To overcome these difficulties, this study proposes a large-deformation topology optimization framework that combines the Third Medium method for implicit modeling of self-contact-like behavior with the arc-length method for nonlinear equilibrium path tracking. Void regions are represented as a fictitious material based on the Third Medium concept, allowing contact-like interactions without explicit contact constraints. Buckling and post-buckling responses are robustly captured using an arc-length solver, enabling stable continuation beyond critical points. A key feature of the proposed approach is the formulation of the Third Medium as a micropolar hyperelastic continuum. Micropolar theory offers well-established formulations for large-deformation kinematics and constitutive modeling, making it well aligned with the requirements of the Third Medium framework. Unlike conventional Third Medium approaches based on Hu–Hu-type regularization, which typically require higher-order finite elements, the micropolar formulation introduces intrinsic bending resistance through additional rotational degrees of freedom. This significantly enhances robustness against mesh distortion and enables stable large-deformation analysis using first-order finite elements. The proposed framework has been implemented in the open-source finite element library Gridap.jl, leveraging its flexible variational formulation and extensibility for nonlinear and multiphysics problems. Numerical examples demonstrate that the combined use of the arc-length method and a micropolar-based Third Medium provides a stable and flexible computational framework for topology optimization under large deformation, accommodating topology changes, self-contact-like behavior, and post-buckling responses in a consistent manner.