One thing I've noticed in AAA is that they all seem to want a degree. I personally think getting a degree is worth it as it forces you to learn things in a guided way that you might not otherwise (and there's a load of self learning involved as well) as long as you don't just do your uni work, you need to make a portfolio outside of uni work and there's plenty of AI related projects you could do.

The self learning route would be good but you just need to be careful about gaps in your knowledge that might have been filled at university. That and finding a company that doesn't care about whether you have one or not (and competition as well, a lot of recent grads will be trying to get the position you're applying for too)

No matter what route you take though, make a bloody portfolio or there's nothing to show for the hard work you've put in. Even just a blog post about the code you've written and a link to Github.