While abilities (combat or otherwise) certainly contribute, and while personality and attitude can help too, I think that what matters most is that the character does actually have the badass qualities they are known for. Sometimes in media, a character apparently possesses a certain trait or ability, but never uses it and, in some unfortunate occasions, has plenty of opportunity to do so but ends up needing to be rescued by someone else. So for me, seeing canonical proof that the character is as kickass as the writer claims is what's most important.