Tim Burton, with his proclivity for the Gothic style and cartoonish fantasy stories, was the perfect choice of director for this realization of Bob Kane's DC Comics series of the same name but he is ably abetted by screenwriters Sam Hamm and Warren Skaaren, the production team headed by Anton Furst, a well-chosen cast (although Kim Basinger brings nothing of note other than her long blond damsel-in-distress tresses) and an atmospheric, if often overbearing, score by Danny Elfman.
The film is a rare achievement for Hollywood in that it combines visual and thematic intelligence with out-and-out action movie entertainment and it became the event of the summer of 1989, grossing more than $250 million in the US alone and making Jack Nicholson, who gives a memorably hyperbolic performance, a very rich man as he had had taken points over an upfront payment.
On the down side the film is often cacophanous and some excuses have to be made for Prince's gratuitous songs (the film was perhaps where he picked up his taste for purple) and Kim Basinger's wardrobe. I had also had trouble with an uncomfortable section in which The Joker and his henchman deface a gallery full of well-known Modernist masterpieces (if Gotham City is a fantasy why have "real" paintings?), and many critics have rightly pointed out the Michael Keaton's Batman was little more than a foil for Nicholson's Joker. Had there been a true match between hero and villain in this film, instead of it only being engaged with in physical form in the grand finale show-down, it would have been a truly remarkable film instead of an impressive exercise in hyper-stylization.
FYI: Burton directed an unremarkable sequel, Batman Returns in 1992 before Warners tried a change of guard, getting Joel Schumacher to direct Batman Forever in 1995 with Val Kilmer as The Caped Crusader. The film was big on Burtonesque SFX but the outcome banal. The franchise did not find its legs again until Christopher Nolan took it away from its cartoon sensibility with a prequel, Batman Begins, in 2005.