First up, the full upgrade to the (as of the time of writing) latest ESXi 6.x release which is 6.7U3 is a two step process.

Download the VMware vSphere Hypervisor v6.7.0 Offline Bundle from my.vmware.com.

Next, download the v6.7.0U3 Offline Bundle by selecting it from the drop-down on the same page.

Upload both images to a storage device by opening up your ESXi UI (https://<vmware-host-ip>/ui) and selecting Storage -> Datastore Browser and pressing Upload. Select an appropriate volume.

Next, enable SSH access by selecting the host from the left hand menu, Actions -> Enable SSH access.

Suspend all VM's and set the host in maintenance mode.

Then log into your host:

ssh <host-ip>

List the available profiles in the 6.7.0 image by running the following command:

esxcli software sources profile list -d /vmfs/volumes/datastore/folder/offline-bundle-name.zip

Do a dry-run install to see that everything looks fine with the standard profile (i.e ESXi-6.7.0-8169922-standard):

esxcli software profile install -d /vmfs/volumes/datastore/folder/offline-bundle-name.zip -p <profilename> --ok-to-remove --dry-run

If everything looks good, perform the update:

esxcli software profile install -d /vmfs/volumes/datastore/folder/offline-bundle-name.zip -p <profilename> --ok-to-remove

Reboot the system

reboot

After the system is back up, if any VM's self-started, suspend them and put the host back into maintenance mode.

Perform the same steps as above, but now using the 6.7.0U3 image:

List the available profiles in the 6.7.0U3 image by running the following command:

esxcli software sources profile list -d /vmfs/volumes/datastore/folder/offline-bundle-name-for-update-3.zip

Do a dry-run install to see that everything looks fine with the standard profile:

esxcli software profile install -d /vmfs/volumes/datastore/folder/offline-bundle-name-for-update-3.zip -p <profilename> --ok-to-remove --dry-run

If everything looks good, perform the update:

esxcli software profile install -d /vmfs/volumes/datastore/folder/offline-bundle-name-for-update-3.zip -p <profilename> --ok-to-remove

Reboot the system:

reboot