Reinforcement learning (RL) has shown considerable potential in autonomous driving (AD), yet its vulnerability to perturbations remains a critical barrier to real-world deployment. As a primary countermeasure, adversarial training improves policy robustness by training the AD agent in the presence of an adversary that deliberately introduces perturbations. Existing approaches typically model the interaction as a zero-sum game with continuous attacks. However, such designs overlook the inherent asymmetry between the agent and the adversary and then fail to reflect the sparsity of safety-critical risks, rendering the achieved robustness inadequate for practical AD scenarios. To address these limitations, we introduce criticality-aware robust RL (CARRL), a novel adversarial training approach for handling sparse, safety-critical risks in autonomous driving. CARRL consists of two interacting components: a risk exposure adversary (REA) and a risk-targeted robust agent (RTRA). We model the interaction between the REA and RTRA as a general-sum game, allowing the REA to focus on exposing safety-critical failures (e.g., collisions) while the RTRA learns to balance safety with driving efficiency. The REA employs a decoupled optimization mechanism to better identify and exploit sparse safety-critical moments under a constrained budget. However, such focused attacks inevitably result in a scarcity of adversarial data. The RTRA copes with this scarcity by jointly leveraging benign and adversarial experiences via a dual replay buffer and enforces policy consistency under perturbations to stabilize behavior. Experimental results demonstrate that our approach reduces the collision rate by at least 22.66\% across all cases compared to state-of-the-art baseline methods.