Data heterogeneity among Federated Learning (FL) users poses a significant challenge, resulting in reduced global model performance. The community has designed various techniques to tackle this issue, among which Knowledge Distillation (KD)-based techniques are common. While these techniques effectively improve performance under high heterogeneity, they inadvertently cause higher accuracy degradation under model poisoning attacks (known as \emph{attack amplification}). This paper presents a case study to reveal this critical vulnerability in KD-based FL systems. We show why KD causes this issue through empirical evidence and use it as motivation to design a hybrid distillation technique. We introduce a novel algorithm, \emph{Hybrid Knowledge Distillation for Robust and Accurate FL (HYDRA-FL)}, \footnote{We will release the open source code with the final version of this paper.}, which reduces the impact of attacks in attack scenarios by offloading some of the KD loss to a shallow layer via an auxiliary classifier. We model HYDRA-FL as a generic framework and adapt it to two KD-based FL algorithms, FedNTD and MOON. Using these two as case studies, we demonstrate that our technique outperforms baselines in attack settings while maintaining comparable performance in benign settings.