Reinforcement learning (RL) achieves strong performance in sequential decision-making but remains brittle under dynamic uncertainty and distributional shifts. Robust Adversarial Reinforcement Learning (RARL) improves robustness via worst-case perturbations, but existing approaches frequently suffer from unstable optimization and degraded value estimation. In particular, overly aggressive adversaries can drive the agent toward uninformative failure states, while adversarial perturbations amplify disagreement between double critics and introduce biased value targets. We propose a unified framework, RACER (Risk-sensitive robust Adversarial critic ConsistEncy-regularized Reinforcement learning), that revisits adversarial RL from a risk-sensitive perspective. First, we introduce a state-dependent adversarial objective that adaptively regulates perturbation strength, suppressing harmful disturbances while preserving informative exploration. Second, we propose critic consistency regularization to reduce disagreement between Q-value estimators and stabilize learning. Comprehensive experiments on challenging continuous control benchmarks demonstrate that RACER consistently improves performance, robustness, and training stability over strong robust RL baselines.