Systematic measurements of Raman scattering and magnetic susceptibility are performed on an optimally doped Bi₂Sr_1.6La_0.4CuO₆ with well characterized change density wave and pesudogap. A pressure-temperature phase diagram is obtained for this superconductor. The superconducting transition temperature T_c is found to initially increase with increasing pressure and then decreases upon heavy compression after passing a maximum at a critical pressure of 15 GPa. Meanwhile, either the charge-density-wave or the pesudogap is suppressed by the applied pressure with the disappearance of their lock-in or opening temperature at the critical pressure. The significant T_c enhancement in the low-pressure region benefits from the suppression of the competing orders. The phonon frequency of the oxygen atoms in the charge reservoir is observed to be closely correlated to the evolution of T_c with pressure. Meanwhile, the emergence of the charge disorder and its growth with pressure are detected after the critical pressure, indicating its unfavorable role to superconductivity. A complete picture for superconductivity with the competing orders, reservoir layer, and charge disorder for a cuprate superconductor is thus established.