Oh. Well. That's easy. The Adventures of Buckaroo Banzai Across the Eighth Dimension. Case closed.
There's B. Banzai, after all. And Reno. And John Parker. And the Jet Car. And Penny Priddy. And the oscillation overthruster. And Professor Emilio Lizardo/Lord John Whorfin, the divergent magnificence of both brought to me by John Lithgow in what may arguably have been his finest role(s). You doubt it? "Laugh while you can, Monkey Boy."
Of course, B. Banzai has all the best lines, partly because they're great pointers for life. "Wherever you go, there you are." "Don't be mean."
Also, B. Banzai and the Hong Kong Cavaliers? They dance just as good as they walk. And they walk with style. Also, loads of narrow belts and ties. And syncopated music. And Perfect Tommy. And ... well, isn't Perfect Tommy enough? (Even though I much prefer Rawhide, and in my personal world he never did run into that particular Red Lectroid, and he's the reason I love Clancy Brown, not the stupid Highlander movie.) And the whole thing's the most brilliant pastiche and paean to Doc Savage that I've yet seen. It's a pity the other hour or so never saw daylight.
And you must read the book by Earl Mac Rauch. Really. It's of inestimable value for all fans of B. Banzai, and makes the movie even more wonderful.
Oh yeah; the rest of the question.
The essential ingredients for a cult classic are (she said, answering it like it was an essay question on a Grade Eleven History final): any suitable combination of off-kilter and generally vaguely scientifictional - or at least, in these degenerate latter days, somewhat niche pop-cultural plot points; attractive character aspects that can either be laughed at, yearned after, or both; one-liners (like whoah!!!); musical themes, any six bars of which, when heard on a radio or over a store sound system, will immediately throw one back into the theatrical experience; and appreciation of the absurd that talented but (possibly) over- or under-medicated writers can mix well and hand over to (possibly) yet-to-be-discovered or shouldn't-be-discovered directors and (definitely) under-appreciated, yet-to-be-discovered. or never-nope-won't-get-discovered actors.
There. I say these things three times, and they are true.