With the increasing adoption of confidential computing, security-sensitive applications are often deployed in confidential virtual machines (CVMs), which reduce reliance on third-party cloud providers. However, privilege attacks originating from the OS remain a significant threat in these environments. Existing finer-grained isolation schemes, such as SHELTER (USENIX SEC’23), provide process-level protection but are still vulnerable to intra-process attacks and potential collusion between the OS and intra-process adversaries. Many current intra-process isolation techniques continue to depend on the OS to manage and enforce isolation domains, leading to a large Trusted Computing Base (TCB). This gap highlights the need for more granular, less trust-dependent confidential computing solutions. In this paper, we present CCAegis, a system that extends the Arm Confidential Compute Architecture (CCA) to enforce intra-process isolation of sensitive data and operations, safeguarding them from both intra-process adversaries and the OS. We employ static analysis to track the flow of sensitive data and identify functions that handle such data. Permission-switching instructions are inserted at the function call and return points, adjusting permissions via the Granule Protection Table (GPT) to ensure that only designated functions can access the isolated data. Notably, CCAegis places trust solely in the Secure Monitor, which configures the GPTs and manages domain switching, thereby minimizing the TCB. We implemented CCAegis on both an official emulator and a real development board to assess its performance. Our experimental results show that CCAegis effectively isolates sensitive data and operations, with performance overheads ranging from 1.01× to 1.43× compared to the original version across real-world cryptographic workloads.