In recent years, effectively modeling multivariate time series has gained significant popularity, mainly due to its wide range of applications, ranging from healthcare to financial markets and energy management. Transformers, MLPs, and linear models as the de facto backbones of modern time series models have shown promising results in single-variant and/or short-term forecasting. These models, however: (1) are permutation equivariant and so lack temporal inductive bias, being less expressive to capture the temporal dynamics; (2) are naturally designed for univariate setup, missing the inter-dependencies of temporal and variate dimensions; and/or (3) are inefficient for Long-term time series modeling. To overcome training and inference efficiency as well as the lack of temporal inductive bias, recently, linear Recurrent Neural Networks (RNNs) have gained attention as an alternative to Transformer-based models. These models, however, are inherently limited to a single sequence, missing inter-variate dependencies, and can propagate errors due to their additive nature. In this paper, we present Hydra, a by-design two-headed meta in-context memory module that learns how to memorize patterns at test time by prioritizing time series patterns that are more informative about the data. Hydra uses a 2-dimensional recurrence across both time and variate at each step, which is more powerful than mixing methods. Although the 2-dimensional nature of the model makes its training recurrent and non-parallelizable, we present a new 2D-chunk-wise training algorithm that approximates the actual recurrence with $\times 10$ efficiency improvement, while maintaining the effectiveness. Our experimental results on a diverse set of tasks and datasets, including time series forecasting, classification, and anomaly detection show the superior performance of Hydra compared to state-of-the-art baselines.