I have one r5.xlarge windows ec2 instance which is attached to 6TB EBS volume and the backup for EBS is taken every week. Now I want a better solution with zero downtime.
Is there a way to implement solution for this and how?
If you want to improve the availability of the large drive, I would recommend FSx. It's not so trivial - you need to set up Active Directory, and your EC2 needs to join AD - but once you have all these components (and there is additional cost as well) - FSx provides significantly higher availability than EBS assuming you're using a multi-AZ setup. More information here
Note that load balancer tags are irrelevant to your question - although to address your first situation you probably need load balancer balancing two EC2 instances