In this work, we study the worst-case consequence of innovation-based integrity attacks with side information in a remote state estimation scenario. A new type of linear attack strategy based on both intercepted and sensing data is proposed and a corresponding stealthiness constraint is characterized. The evolution of the remote estimation error covariance is derived in the presence of the proposed malicious attack, based on which the worst-case attack policy is obtained in closed form. Furthermore, the system estimation performance under the proposed attack is compared with that under the existing attack strategy to determine which attack is more critical in deteriorating system functionality. Simulation examples are provided to illustrate the developed results.