For this you will need:
Zipped file containing the latest firmware version (here)
Blank, formatted USB Stick
The first step is to ensure that you USB stick if formatted as 'FAT32'. Plug the USB into a computer, right click the USB Icon and select 'Format'. Make sure 'FAT32' is selected, then click 'format'.
Copy the firmware file (.TGZ) onto this newly formatted USB stick,
With the printer turned OFF, insert the USB stick into the printer. Then turn the printer ON, and allow it to install. The screen may stay on 'Downloading', but wait for the 'Complete' screen to show. Once the update is successful, turn the printer OFF once again.
Unplug the USB stick, and switch the printer back ON again. Your Adventurer 4 should now be up to date, and you can confirm this by tapping 'Settings' > 'Page 2' > 'About' and checking the firmware version.