Learn English – word for a person that can do impossible things

A person who is hard to put up with may be described as insufferable. A person who lacks graceful behaviour or acceptable/pleasing social skills is uncouth.

Perhaps the word is not specific enough, but I'd simply suggest challenging.

Something challenging is demanding, so perhaps it doesn't quite stretch to being "near impossible", however a challenge suggests something which is "fun to try". I suppose it depends whether you are looking for an obscure or common word. HTH