You can gain access to Tanzu Kubernetes Clusters via SSH by using one of the below methods. Each method assumes you have access to the supervisor cluster control plane VMs.
VMware vCenter Server 7.0.x
SSH to Tanzu Kubernetes Cluster Nodes as the System User Using a Private Key
https://techdocs.broadcom.com/us/en/vmware-cis/vsphere/vsphere-supervisor/7-0/vsphere-with-tanzu-configuration-and-management-7-0/connecting-to-vsphere-with-tanzu-clusters/ssh-to-tanzu-kubernetes-cluster-nodes-as-the-system-user.html
SSH to Tanzu Kubernetes Cluster Nodes as the System User Using a Password
https://techdocs.broadcom.com/us/en/vmware-cis/vsphere/vsphere-supervisor/7-0/vsphere-with-tanzu-configuration-and-management-7-0/connecting-to-vsphere-with-tanzu-clusters/ssh-to-tanzu-kubernetes-cluster-nodes-as-the-system-user-using-a-password.html