Unsigned distance fields (UDFs) allow for the representation of models with complex topologies, but extracting accurate zero level sets from these fields poses significant challenges, particularly in preserving topological accuracy and capturing fine geometric details. To overcome these issues, we introduce DCUDF2, an enhancement over DCUDF--the current state-of-the-art method--for extracting zero level sets from UDFs. Our approach utilizes an accuracy-aware loss function, enhanced with self-adaptive weights, to improve geometric quality significantly. We also propose a topology correction strategy that reduces the dependence on hyper-parameter, increasing the robustness of our method. Furthermore, we develop new operations leveraging self-adaptive weights to boost runtime efficiency. Extensive experiments on surface extraction across diverse datasets demonstrate that DCUDF2 outperforms DCUDF and existing methods in both geometric fidelity and topological accuracy. We will make the source code publicly available.