The beauty of the Batman Begins script is that with a few adjustments, (Specifically having Ducard mention on the train sequence that he's "Not Ra's al Ghul either," and flashing back to the man Bruce saw in prison, walking into the compound the next day, and leaving Ducard with him after the fire, omiting the Joker cards from Gordon's speech about escalation, and introducing Jack Napier as Grissom's right-hand man without him doing much in the movie except showing up), you can use the actual Batman '89 script for the direct sequel, so long as you throw in a Vicki Vale-Bruce Wayne-Rachel Dawes-Billy Dee Williams Harvey Dent love square. For the Sequel Hook to that movie, have Dent wake up in the hospital with Rachel dead, blaming Batman for what happened, while a poster shows the Haley Circus coming featuring the Flying Graysons coming to town in a few months.
The third movie features the villains of Batman Forever, but with a rather darker tone. Harvey is a deranged serial killer using the toss of the coin to dertmine the final fate of his (asshole) victims. Also on the streets is a vengeful downsized toymaker named Edward Nygma who locks other (asshole) victims in trick question deathtraps a-la-Jigsaw from the Saw series, and finances his activities with heists where he leaves obscure clues and puzzles to taunt the police. One of those robberies causes the death of most of the Flying Graysons, leading its youngest and only survivor to hunt down the killer, and end up in over his head. It ends with Harvey dead, Batman and Robin taking the fall, the Bat Signals being smashed, and Batman going underground.
The fourth movie features Dick Grayson off to college, the rise of a new underworld boss called "Black Mask" with the help of an assassin named Deadshot (or maybe Deathstroke) with ties to the League of Shadows, plus this annoying cat burglar/marital artist named Selina Kyle, and these two kids, one of them the daughter of Commissioner Gordon, who've discovered Bruce's secret identity as Batman. Then all hell breaks loose when Gotham Stadium looses its field and the real Ra's al Ghul reveals himself threatening Gotham with a nuclear weapon...