Deep reinforcement learning (DRL) has demonstrated remarkable success in developing autonomous driving policies. However, its vulnerability to adversarial attacks remains a critical barrier to real-world deployment. Although existing robust methods have achieved success, they still suffer from three key issues: (i) these methods are trained against myopic adversarial attacks, limiting their abilities to respond to more strategic threats, (ii) they have trouble causing truly safety-critical events (e.g., collisions), but instead often result in minor consequences, and (iii) these methods can introduce learning instability and policy drift during training due to the lack of robust constraints. To address these issues, we propose Intelligent General-sum Constrained Adversarial Reinforcement Learning (IGCARL), a novel robust autonomous driving approach that consists of a strategic targeted adversary and a robust driving agent. The strategic targeted adversary is designed to leverage the temporal decision-making capabilities of DRL to execute strategically coordinated multi-step attacks. In addition, it explicitly focuses on inducing safety-critical events by adopting a general-sum objective. The robust driving agent learns by interacting with the adversary to develop a robust autonomous driving policy against adversarial attacks. To ensure stable learning in adversarial environments and to mitigate policy drift caused by attacks, the agent is optimized under a constrained formulation. Extensive experiments show that IGCARL improves the success rate by at least 27.9% over state-of-the-art methods, demonstrating superior robustness to adversarial attacks and enhancing the safety and reliability of DRL-based autonomous driving.