Across various industries, credential verification stands as a critical requirement, yet traditional approaches face limitations in security, privacy, and interoperability. Although recent blockchain innovations promise decentralization, deploying them independently in institutions creates data isolation. While there are theoretical frameworks, lack of practical studies achieving a balance between credential mobility and privacy is noteworthy. This paper introduces CrossCert, a privacy-focused cross-chain system for verifying credentials between educational and employer blockchains. By incorporating zero-knowledge proofs, CrossCert facilitates anonymous checks without disclosing user details. Extensive experiments have consistently demonstrated CrossCert's real-time performance, even within blockchain limitations. Its security features, including cryptographic proofs and on-chain data management, demonstrate strong resilience against typical attacks and web vulnerabilities. CrossCert pioneers bridging the research gap between education, employment, and privacy, striving to achieve a balanced balance of credential accessibility and ethical information practices with its innovative cross-chain architecture. The system hence merits further research as a feasible solution to streamline decentralized credential validation across diverse stakeholders.