This paper considers the time-varying formation (TVF) tracking issue of a class of multiagent systems (MASs) with input saturation. Meanwhile, the prescribed transient and steady-state performance of MASs is guaranteed. Compared to the existing prescribed performance control (PPC) approaches, the maximum convergence time of the designed algorithm is preassigned. To save network resources, an event-based protocol is introduced to achieve lower information communication frequency, where Zeno behavior is excluded. Furthermore, an improved control strategy is employed where an auxiliary system is designed to improve the performance under actuator saturation. According to Lyapunov stability theory, the expected practical TVF tracking control problem is solved for the MASs. Finally, the effectiveness of the designed schemes is demonstrated by the simulation examples.