BFT consensus that uses Trusted Execution Environments (TEEs) to improve the system tolerance and performance is gaining popularity. However, existing works suffer from TEE rollback issues, resulting in a tolerance-performance tradeoff. In this paper, we propose Achilles, an efficient TEE-assisted BFT protocol that breaks the tradeoff. The key idea behind Achilles is removing the expensive rollback prevention of TEEs from the critical path of committing transactions. To this end, Achilles adopts a rollback resilient recovery mechanism, which allows nodes to assist each other in recovering their states. Besides, Achilles follows the chaining spirit in modern chained BFT protocols and leverages customized chained commit rules to achieve linear message complexity, end-to-end transaction latency of four communication steps, and fault tolerance for the minority of Byzantine nodes. Achilles is the first TEE-assisted BFT protocol in line with CFT protocols in these metrics. We implement a prototype of Achilles based on Intel SGX and evaluate it in both LAN and WAN, showcasing its outperforming performance compared to several state-of-the-art counterparts.