The idiom "through fire, water and brass pipes" came into Russian through other languages reflecting ancient traditions of trials by ordeal. Trials by "fire and water" is a popular subject, which can be googled to find a ton of references. The brass part sounds original but it also came from ancient tradition, particularly Egyptian cult of Isis. See this reference to Heckerthorn's "The Secret Societies of All Ages and Countries (1897)" book, pp.72-73. He describes the trials by fire, water and air (in correct order). The air part includes the brass rings.
I think in the Russian namesake movie, and in modern understanding "brass pipes" became "trumpets" completely changing the meaning of the last part from an ordeal to "fame". I think that this substitution happened relatively recently, maybe in past 50 years. Also, say 100 years ago, the meaning of the whole idiom had a negative connotation, which is lost these days. It used to refer to a shrewd person, who can get his way.