During terminal guidance, the attack platform is provided with high-resolution image of the target area through the application of synthetic aperture radar (SAR). Additionally, the stealth trajectory with low observability can significantly impact mission success. This paper considers both missile-borne SAR imaging performance and stealth performance as influencing factors for terminal trajectory optimization, which is modeled as a constrained multi-objective optimization problem. With the successful application of the pseudospectral method in the solution of optimal control problems, the hybrid genetic algorithm pseudospectral optimization (HGAPO) framework is proposed. The problem is decomposed to several single-objective optimal control problems, which can generate a specific initial population for the genetic algorithm to obtain a set of Pareto-optimal solutions. Finally, the numerical simulations demonstrate the effectiveness of the proposed optimization approach compared with the benchmark scheme.