Distribution shifts and minority subpopulations frequently undermine the reliability of deep neural networks trained using Empirical Risk Minimization (ERM). Distributionally Robust Optimization (DRO) addresses this by optimizing for the worst-case risk within a neighborhood of the training distribution. However, conventional methods depend on a single, global robustness budget, which can lead to overly conservative models or a misallocation of robustness. We propose a variance-driven, adaptive, sample-level DRO (Var-DRO) framework that automatically identifies high-risk training samples and assigns a personalized robustness budget to each based on its online loss variance. Our formulation employs two-sided, KL-divergence-style bounds to constrain the ratio between adversarial and empirical weights for every sample. This results in a linear inner maximization problem over a convex polytope, which admits an efficient water-filling solution. To stabilize training, we introduce a warmup phase and a linear ramp schedule for the global cap on per-sample budgets, complemented by label smoothing for numerical robustness. Evaluated on CIFAR-10-C (corruptions), our method achieves the highest overall mean accuracy compared to ERM and KL-DRO. On Waterbirds, Var-DRO improves overall performance while matching or surpassing KL-DRO. On the original CIFAR-10 dataset, Var-DRO remains competitive, exhibiting the modest trade-off anticipated when prioritizing robustness. The proposed framework is unsupervised (requiring no group labels), straightforward to implement, theoretically sound, and computationally efficient.