Multi-legged climbing robots have appealing applications to extreme terrain on asteroids with the microgravity. The robot usually consists of multiple legs and grippers with hierarchical arrays of microspines. The dimensional optimization of the robot with the complicated structure is still a challenge. This paper proposes a multi-parameter grouping optimization method for the multi- legged climbing robot based on performance atlas. First, the structure of the multi-legged climbing robot is described and the kinematic model is established. Second, four performance evaluation indices of the robot, namely the global conditioning index (GCI), the global stiffness index (GSI), the global transmission index(GTI), and the global adhesion efficiency index (GAEI), are derived from the kinematic equations. Third, 11 dimensional parameters of the robot are catergorized into three groups and the detailed optimization process is poposed. Non-dimensional design spaces of three groups of parameters are established and performance atlases regarding the aforementioned evaluation indices are drawn. Finally, the optimal diemensions of the robot are obtained. Besides, the proposed multi-parameter optimization method can be further applied to other legged robots, and the global adhesion efficiency index can be used to guide the design of other grippers.