When migrating a VM from a legacy 3-tier solution using VMware ESXi to AHV, two methods can be employed effectively: deploying the Move appliance and importing the .vmdk into the Image Service. Deploying the Move appliance is a suitable tool provided by Nutanix for seamless migrations. Importing the .vmdk into the Image Service simplifies the process by allowing the disk image files to be moved directly into the Nutanix environment. These methods avoid potential complexities and ensure a smooth migration process.