Accurate prediction of the Remaining Useful Life (RUL) in machinery can significantly diminish maintenance costs, enhance equipment up-time, and mitigate adverse outcomes. Data-driven RUL prediction techniques have demonstrated commendable performance. However, their efficacy often relies on the assumption that training and testing data are drawn from the same distribution or domain, which does not hold in real industrial settings. To mitigate this domain discrepancy issue, prior adversarial domain adaptation methods focused on deriving domain-invariant features. Nevertheless, they overlook target-specific information and inconsistency characteristics pertinent to the degradation stages, resulting in suboptimal performance. To tackle these issues, we propose a novel domain adaptation approach for cross-domain RUL prediction named TACDA. Specifically, we propose a target domain reconstruction strategy within the adversarial adaptation process, thereby retaining target-specific information while learning domain-invariant features. Furthermore, we develop a novel clustering and pairing strategy for consistent alignment between similar degradation stages. Through extensive experiments, our results demonstrate the remarkable performance of our proposed TACDA method, surpassing state-of-the-art approaches with regard to two different evaluation metrics. Our code is available at https://github.com/keyplay/TACDA.