Use youtube-dl directly to download the video (thanks @meepybub!) Example:
youtube-dl -u <youremailaddress@example.com> "https://vimeo.com/ondemand/<video>"
If variant 1 doesn't work, try this.
Login to Vimeo and get the cookies.txt file using this Chrome plugin
Use youtube-dl to download the video Example:
youtube-dl "https://vimeo.com/ondemand/<video>" --cookies cookies.txt
I had a lot of success with this repo for private videos: https://github.com/Tusko/vimeo-private-downloader
This was my way to resolve, hope it helps;
open up dev tools, in the network tab, filter for master.json, start the video to make sure you find the right url, right click it and copy url.
then use;
youtube-dl -o file.mp4 "URL"
before you hit enter, edit the URL so it ends in .mpd instead of .json