How to terminate CloudWatch service?

Unfortunately, CloudWatch cannot be completely terminated or disabled as it is an integral part of AWS services. Many AWS services automatically send logs and metrics to CloudWatch for free. However, you can take steps to minimize any potential charges related to CloudWatch:

1. Delete any CloudWatch alarms you may have created.
2. Remove any CloudWatch dashboards you've set up.
3. Ensure that none of your AWS resources are logging to CloudWatch.
4. Disable any detailed monitoring options you might have enabled for services like EC2, as these can incur additional charges.
5. Review your AWS bill and Cost Explorer to identify any specific CloudWatch usage that's generating charges.
6. Check for and delete any custom metrics or filters you may have created, especially for services like S3.

Remember that basic monitoring metrics sent by AWS services by default are typically included in the free tier. If you're still concerned about potential charges, you can review your CloudWatch usage in the AWS Cost Explorer to ensure you're not incurring any unexpected costs.

If you want to completely eliminate the possibility of any AWS charges, including those from CloudWatch, the most definitive action would be to close your AWS account entirely. However, this is a drastic step and should only be taken if you're certain you won't need any AWS services in the future.
Sources
Can't remove CloudWatch service | AWS re:Post
Cancel AmazonCloudWatch altogether | AWS re:Post
Disabling Cloudwatch | AWS re:Post