Is the “fear of death” the most powerful impulse of the spirit for Batman?

Is the fear of death the most powerful impulse of the spirit for Batman in Dark Knight Rises

No. Bruce Wayne ends up showing us his humanity in many ways, including a few of his fears, in this movie. However, considering that he fights and puts himself in harm's way as he does, a fear of death is not one of his fears. Although he trusts the technology behind his gear, and the design behind the technology, a fear of death would hamper his ability to perform his death-defying stunts and acrobatics.

Is the fear of death the most powerful impulse of the spirit superheroes in other films

I suppose that one could argue that Tony Stark is kept alive by the magnet in his chest that he improved and maintains because he has a fear of death, and that the creation of his suit in the first Iron Man movie was also because he feared dying (being killed) in that cave. Of course, he wanted to do a lot of damage on the way out, and he feared that Stark Industry weapons would continue to be used against American troops and innocent civilians... but that's a different fear. However, I don't believe that the Green Lantern is motivated by a fear of death at all. I don't believe Superman in any of his movie incarnations is motivated by a fear of death. I know the Hulk isn't motivated by a fear of death. I suspect that a fear of losing his sense of humor is the most powerful motivating factor in Spiderman's life.

In general, I believe that motivations, or what drives the Individual Superheroes, are as different and individual to each Hero as the Heroes are themselves. I mean, X-Men aren't quite Superheroes in the same sense that Batman, Superman, and Spiderman... but you can definitely say that a fear of death is not in Wolverine's mental bag of tricks.

Is there a philosophical understanding of fear and in particular fear of death that supports the idea and development of the superhero?

Again, it depends on the Superhero. In the case of Green Lantern, the understanding and study of fear is integral to the development of the entire Green Lantern Corps. Fear had it's own color (Yellow) and got a ring, was the motivation behind a Supervillan, etc. Fear in general, and specific fears, don't play as much of a part in many of the Superman movies... although Superman giving up his power to settle down with Lois Lane might have been out of fear of turning her to mush during some Supersex. Probably not though. The development of Doctor Manhattan was not born of a fear of death. He pretty much started out as dead, or believing himself dead. As he once said, reconstituting himself from scattered atoms was the first thing he figured out how to do.

You can say that there is typically a moral message in each Superhero storyline, and that there is a moral struggle each Superhero faces. However, you can't globally say that all superheroes struggle with a fear of death. Some would welcome it at one time or another. I'm sure Bruce Banner wished more than a few times early on that he could die rather than become the Hulk... until he got some kind of handle on it. But with the Hulk, the story is definitely more about Rage and dealing with it properly, than it is about fear and the fear of death.

Edit It is important to note that Bruce Wayne's statement...

I do fear death. I fear dying in here, while my city burns, and there's no one there to save it.

... is more a fear of being impotent (in being able to save Gotham) than an actual fear of death. I mean, I realize he says the words "I do fear death, I fear dying here" but taken alone out of context, you miss what it is he actually fears, which is the death of Gotham, not the death of Bruce Wayne or the death of Batman.