I can point to real products in the wild demonstrating that I can deliver a shipping app from the idea stage with no hand holding, and I can put together an entire sentence over the phone. But beyond that, there's nothing special that I do that other developers can't, except ask to be paid a market rate.
And to head off the inevitable comment about contracting being unsustainable and feast-or-famine, I recently ended a 5 year, full time remote gig at that aforementioned Bay Area rate. It's certainly doable, for a regular dev off the street. You just need to be able to prove that you're good at what you do.
communication and response time is also pretty huge. Employers love people that get right back to them with details, or at least a response to let them know they are working on it.
I myself am a contractor, but I also hire other contractors under me, so I know a little bit about the hiring of contractors process. Most of the time I start with something small, and work them into the larger jobs. For instance, I'll start them with debugging problem areas of our website / app. If they do well and fit with our remote team, I will give them more and more. Money doesn't matter nearly as much as being able to get the job done so if someone quotes $100/hour vs $75/hour its not even a consideration.
for instance, getting a really nice high def headshot on a website with actual samples of your apps, designs, or projects can really go a long way. (as opposed to an email with written descriptions of what you've done). Active Github pages are great, but its also nice to make a "demo page" of all of your end products.
lastly, it is great to see passion. this might be an active Twitter profile, a blog where you write a monthly post on what you are working on, or even an active Instagram where you take cool pics of your products and interact with others. it isn't mandatory but it definitely sticks out, big time.
I don't make nearly as much as many of the people in here, but I do live a comfortable life where I can travel and have some nice things, and I've been doing so for the last 10 years.