For a software developer role, you generally need a degree. Some of the harder algorithmic aspects can be super hard to learn on your own. However, any degree can be trumped by experience. I see github as the absolute best resume available.
It is possible, but very difficult to get any job in upper management without a degree.
Disclaimer: I've worked professionally in tech for 10+ years, lack a college education, and am very successful. However, I did a technical job for 4 years in the US Army.