That's an interesting angle that made me give some serious thought to what I consider badass. Feats of strength or cunning are one thing and often amusing on their own but most of my favorite badass moments come from a real sense of compassion expressed with extreme conviction.
Like the example from Hunter x Hunter I posted earlier in the thread. I can't go into it too much without spoiling the show but you get a great sense of how much Leorio truly cares for his friends.
Or Giant Robo which I also mentioned, which has just about every flavor of badass but my favorite scenes from that show usually involve self-sacrifice or characters working together in extremely dangerous situations.
So to me the most badass thing is being excellent to one another even under adverse circumstances, or something.
For me badassery is kinda what kind of air you are putting around you. For example Hellsing. There is two literal army going at each others throat with their own special individuals and such and when Alucard makes his entrance everyone without an exception targets him instinctively most of them only heard of Alucard most of them never saw or fight against him and only know him through talking yet when he started to chant his release everyone friend or enemy tried to stop him this is something not many (if any) anime character could achieve.