The problem of global prescribed performance control (PPC) for the multi-input multi-output (MIMO) block-triangular systems with unknown nonlinearities and mismatched disturbances is investigated in this article. The design purposes lie in the independent prescribed settling times and the independent control gains. They cannot be fulfilled by the existing solutions and become more challenging under the radially unbounded system nonlinearities. Therefore, a novel global PPC strategy is developed in this article. Herein, a family of inverse-proportional-type performance functions is designed to independently prescribe the settling times for the tracking errors and the intermediate errors. Moreover, to verify the feasibility of the independent control gains, a unified performance analysis grounded on a barrier Lyapunov function with nonuniform weights and the proof by contradiction is conducted. In addition, the proposed approach preserves the fast and accurate tracking capacity and the unique simplicity of PPC, without approximation or identification. A pair of experiments on a 2-DOF serial flexible link robot is performed to validate the efficacy and advantages of the control approach.