Cloud computing and big data analytics have transformed enterprise operations, yet traditional perimeter-based security models fail in distributed, multi-cloud environments. Zero Trust Architecture (ZTA) addresses these limitations by enforcing continuous verification and identity-centric controls. This study examines Zero Trust principles applied to cloud-based big data systems, focusing on micro-segmentation, policy-as-code enforcement, and continuous authentication mechanisms. We propose a reference architecture integrating identity governance, least-privilege access, and adaptive trust scoring across ingestion, processing, storage, and orchestration planes. The framework demonstrates how policy-driven controls, combined with AI-based anomaly detection, can mitigate insider threats, lateral movement, and data exfiltration in dynamic analytics workloads. Implementation challenges—including verification latency, multi-cloud heterogeneity, and dynamic data classification—are analyzed alongside deployment best practices. Results indicate that Zero Trust provides scalable, auditable protection for petabyte-scale data pipelines while maintaining compliance and operational resilience in hybrid cloud environments.