Security is a crucial issue for cyber-physical systems, and has become a hot topic up to date. From the perspective of malicious attackers, this article aims to devise an efficient scheme on false data-injection (FDI) attacks such that the performance on remote state estimation is degraded as much as possible. First, an event-based stealthy FDI attack mechanism is introduced to selectively inject false data while evading a residual-based anomaly detector. Compared with some existing methods, the main advantage of this mechanism is that it decides when to launch the FDI attacks dynamically according to real-time residuals. Second, the state estimation error covariance of the compromised system is used to evaluate the performance degradation under FDI attacks, and the larger the state estimation error covariance, the more the performance degradation. Moreover, under attack stealthiness constraints, an optimal strategy is presented to maximize the trace of the state estimation error covariance. Finally, simulation experiments are carried out to illustrate the superiority of the proposed method compared with some existing ones.