A zero-temperature magnetic-field-driven superconductor to insulator transition (SIT) in quasi-two-dimensional superconductors is expected to occur when the applied magnetic field crosses a certain critical value [S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Rev. Mod. Phys. 69, 315 (1997); A. M. Goldman, Int. J. Mod. Phys. B 24, 4081 (2010)]. A fundamental question is whether this transition is due to the localization of Cooper pairs or due to the destruction of them. Here we address this question by studying the SIT in amorphous WSi. Transport measurements reveal the localization of Cooper pairs at a quantum critical field B1c (Bose insulator), with a product of the correlation length and dynamical exponents zν∼4/3 near the quantum critical point. Beyond B1c, superconducting fluctuations still persist at finite temperatures. Above a second critical field B2c>B1c, the Cooper pairs are destroyed and the film becomes a Fermi insulator. The different phases all merge at a tricritical point at finite temperatures with zν=2/3. Our results suggest a sequential superconductor to Bose insulator to Fermi insulator phase transition, which differs from the conventional scenario involving a single quantum critical point.