Your best approach will be just to hire somebody off a freelancing website.
Of course, it's not free!
You're obviously looking for something that costs you no money but, I'm sorry to break this to you, considering the
amount of work you need done, you need to spend a few bucks.
Somebody above mentioned Fiberr might be a good option.
There are some server providers that use complicated and powerful tools and rent out themselves for 5 bucks a pop.
I think when it comes to cost-containment that is probably your best alternative.
You'll definitely will not be able to get a comprehensive backlink analysis for absolutely free.
There are also some cheap backlink watcher-analyzer tool sub, but they suck.
They're very limited.
They only show a tiny fraction of your overall backlink footprint.