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Bit-flip attacks (BFAs) have attracted substantial attention recently, in which an adversary could tamper with a small number of model parameter bits to break the integrity of DNNs. To mitigate such threats, a batch of defense methods are proposed, focusing on the untargeted scenarios. Unfortunately, they either require extra trustworthy applications or make models more vulnerable to targeted BFAs. Countermeasures against targeted BFAs, stealthier and more purposeful by nature, are far from well established. In this work, we propose Aegis, a novel defense method to mitigate targeted BFAs. The core observation is that existing targeted attacks focus on flipping critical bits in certain important layers. Thus, we design a dynamic-exit mechanism to attach extra internal classifiers (ICs) to hidden layers. This mechanism enables input samples to early-exit from different layers, which effectively upsets the adversary's attack plans. Moreover, the dynamic-exit mechanism randomly selects ICs for predictions during each inference to significantly increase the attack cost for the adaptive attacks where all defense mechanisms are transparent to the adversary. We further propose a robustness training strategy to adapt ICs to the attack scenarios through simulating BFAs during the IC training phase, to increase model robustness. Extensive evaluations over four well-known datasets and two popular DNN structures reveal that Aegis could effectively mitigate different state-of-the-art targeted attacks, reducing attack success rate by 5-10x, significantly outperforming existing defense methods. We open source the code of Aegis.