A character believes him/herself to be badass, but is actually inept even by ordinary standards.
There are some people you just shouldn't mess with. People who could tear you limb from limb as easy as looking at you. People who walk through life with the proverbial Big Stick slung across their backs. And then there are the people who think they're those sorts of people. A Self Styled Badass is a character who does not qualify as a big fish even in a small pond, but is nevertheless convinced of their own ability. You can expect them to attempt to show off their skills with feats that range from unimpressive to disastrous, or step into fights where they're completely out of their depth, sometimes even repeatedly without learning their lessons. Compare Miles Gloriosus, who talks the talk but knows better than to try and live up to their own hype.