Just going by the script drafts, there was no deleted Joker/Grissom scene, and no "Hiding from the Joker" scene.
The only deleted scenes we have access to are the aforementioned "rescuing the girl" and "Exteneded Press Conference" scenes that are presented in the middle of parts 2 and 3 of the SE DVD "Shadows of the Bat" documentary.
Various behind-the-scenes footage through the years (including the SE DVD feature "On the set with Bob Kane" and the Topps cards) shows the Bob/Batman fight.
The SE DVD featurette with the deleted Robin scene is a sequence that didn't make it past the script stage. The scene still existed, even once new drafts cut Robin out, though. The DVD feature doesn't show the setup for the scene, however, it appears in the novelization. The scene originally took place right after the scene in Vicki's apartment, originally set near dusk, and after "shooting" Bruce, (Who instead deflected the bullet accidently with the utility belt inside his shoulder-bag) the Joker takes Vicki to go photograph him taking the mayor hostage. Then, as the DVD featurette shows, Bruce wears a ski-mask from Vicki's apartment and, with his belt, swoops over the Gotham rooftops after the Joker, calling Alfred, who drives by in an unmarked vehicle and throws Bruce his costume (The novel actually has his dismount from his horse and get into the back seat of Alfred's car to change), Batman then continues the pursuit in costume. The horse was acquired from a mounted policeman, who faints due to the Joker drugging all of the cops in the city with doctored coffee. The Joker gets to the 200th birthday gala and takes the mayor hostage, revealing that, instead of a statue of John T. Gotham, the dedicated statue was of the Joker. Batman appears and forces the Joker to run away in a rather exciting scene.
But after the mishap with Sean Young involving horses, the sequence was reluctantly cut from the film.