This paper confronts the formation control problem for a multi-robotic fish system with event-triggered communication mechanism. A three-dimensional (3-D) distributed formation control framework is proposed to drive the robotic fish agents to an anticipated configuration aligning with a moving target. In particular, a consensus-based formation control law is intended to realize the two-stage formation control process. Taking the energy-constrained occasions into consideration, the communication structure and event-triggered protocols are initially tailored. Meanwhile, the Lyapunov function is employed and the globally asymptotic stability of the proposed method is fully demonstrated. Afterwards, making use of the local measurements of triggering times, the unscented Kalman filter (UKF) is introduced and a novel model-based event-triggered mechanism is put forward to further mitigate otiose communication consumption. Finally, adequate simulations and experiments are carried out to verify the effectiveness and robustness of the proposed scheme. Thereby, the proposed formation control frame offers great potential for future practical marine operations of the underwater multi-agent systems.