In-memory Computing (IMC) using Phase Change Memory (PCM) has proven to be effective for efficient processing of Deep Neural Networks (DNNs). However, with the use of multi-level cell PCM (MLC-PCM) in NVMs-based accelerators, errors due to resistance drift in MLC-PCM can severely degrade the DNNs accuracy. In this paper, an analysis of the impact of resistance drift errors on accuracy of MLC-PCM based DNN accelerator shows that the drift errors alone can significantly impact the accuracy. This paper proposes Hydra, which is a hybrid resistance drift resilient architecture for MLC-PCM based DNN accelerators which use IMC for efficient computations. Hydra utilizes Tri-level cell PCM, which has a negligible resistance drift error rate, to store the critical bits of DNNs parameters and MLC-PCM (4-level cell), which has a higher error rate (but offers more storage density), for the non-critical bits. Experimental results on various DNN architectures, configurations and datasets show that, with the presence of resistance drift errors in PCM, Hydra can maintain the baseline accuracy of DNNs for up to 1 year (resistance drift is time-dependent), whereas conventional drift tolerance techniques lead to a significant accuracy drop in just a few seconds.