Dimensionality plays a central role in high-temperature superconductivity (HTS). Layered cuprate superconductors hold the record of T_c at ambient pressure. Cuprates in the two-dimensional (2D) limit would provide valuable insights on the nature of HTS and offer unprecedented tunability in their material properties. Half-unit-cell-thick single crystal of Bi₂Sr₂CaCu₂O_8+δ (referred to as monolayer Bi-2212) is such an ideal 2D system. Here we fabricate transport devices from monolayer Bi-2212 samples obtained by exfoliation and study the evolution of superconductivity as the dimensionality and doping level is varied. We find that superconductivity remains intact in monolayer Bi-2212. Finite size scaling analysis at superconductor-to-insulator transition (SIT) reveals distinct critical behaviors at different disorder levels. Our study leads to a unified picture of SITs previously reported in cuprate systems.