Which would be the ideal choice, literal option:
A JAVI BROTHERS MOVIES
A JAVI BROTHER'S MOVIES
A JAVI BROTHERS' MOVIES
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First of all, you can't say "a movies". It's either "a (...) movie" if it's one movie, or "(...) movies" when there's more. Let's assume the second.
Otherwise, all three are correct, but in different contexts.
You'd say "Javi brothers' movies" when referring to the actual group of people who make the films. Like "Wachowski brothers' movies", or "Coen brothers' movies".
You'd say "Javi Brothers movies" when "Javi Brothers" is a corporation or otherwise a singular entity - "Javi Brothers" then functions as an attributive noun. Compare "Warner Brothers movies".
You'd say "Javi brother's movies" when one of the brothers has gone out and made films on his own. So, for example, if Joel Coen decided to ditch Ethan, you could refer to his films as "Coen brother's movies". It would be a somewhat odd construction, but correct.
That's all, of course, assuming that we're taking about creating movies, not owning them - for example, on DVDs :)