Continual Test Time Adaptation (CTTA) has emerged as a critical approach for bridging the domain gap between the controlled training environments and the real-world scenarios, enhancing model adaptability and robustness. Existing CTTA methods, typically categorized into Full-Tuning (FT) and Efficient-Tuning (ET), struggle with effectively addressing domain shifts. To overcome these challenges, we propose Hybrid-TTA, a holistic approach that dynamically selects instance-wise tuning method for optimal adaptation. Our approach introduces the Dynamic Domain Shift Detection (DDSD) strategy, which identifies domain shifts by leveraging temporal correlations in input sequences and dynamically switches between FT and ET to adapt to varying domain shifts effectively. Additionally, the Masked Image Modeling based Adaptation (MIMA) framework is integrated to ensure domain-agnostic robustness with minimal computational overhead. Our Hybrid-TTA achieves a notable 1.6%p improvement in mIoU on the Cityscapes-to-ACDC benchmark dataset, surpassing previous state-of-the-art methods and offering a robust solution for real-world continual adaptation challenges.