This question discusses formal synonyms for "badass" as an adjective, but I am asking for a noun usable in a somewhat formal setting with the same connotation and meaning. A single word would be preferable, but a short phrase is acceptable.
I personally would show admiration for a badass in a formal setting by saying something like "Joe Bloggs is pretty indomitable"
impossible to defeat or discourage
Full Definition of INDOMITABLE
incapable of being subdued : unconquerable
A combination of the words bold and audacious; excellent, admirable, or attractive
Obviously the latter is also US informal but removes the "ass" element.