The robotic fish of BCF/MPF hybrid propulsion achieves efficient and stable swimming through the synergistic control of pectoral fins and body. However, the control problem has been less studied of fins-body coupling with multiple degrees of freedom. This study focuses on the development and synergistic control of robotic fish with fins-body. First, a robotic fish with pectoral fin and body co-propulsion was designed, and a gait controller of fin-body synergic was constructed by a central pattern generator (CPG). Specifically, the control parameters were simplified, and the synergic movement was realized of fin-body coupling with multiple degrees of freedom. Secondly, the dataset was obtained with computational fluid dynamics (CFD) simulations and six-dimensional force sensors, and the offline hydrodynamic model was obtained by bidirectional long-short-time memory networks (BiLSTM) identification, which is the relationship between the control parameters and force/torque of the robotic fish. The model parameters were updated online with experimental data. Finally, a control framework is constructed for offline-online model and event-triggered nonlinear model predictive control (ENMPC), which compensates for the driving force of the robotic fish, achieves tracking trajectory precisely, and reduces the computational cost.