The Riddler has kidnapped, of all people, a pig farmer. Batman, as ever, must solve a riddle on the display of whatever deathtrap the farmer is strapped to in order to save the poor man. Hence:
My beginning is a giant's satellite.
My third is, without what is most common, all we are left with.
My ending is the beginning of all things.
My whole is one of existence, of denial, of decay.
What am I?
I think you are
IOWA.
My beginning is a giant's satellite.
IO is a moon (satellite) of Jupiter (a gas giant).
My third is, without what is most common, all we are left with.
W is all that's left of "we" after the most common letter (E) is removed.
My ending is the beginning of all things.
A is the beginning of "all things".
My whole is one of existence, of denial, of decay.
Iowa is a US state - perhaps where the farmer comes from? As @Rubio suggests in a comment, the significance of this line may be that the word "state" often precedes "of existence", "of denial", or "of decay".
As you can probably tell from the timestamps, this riddle was fairly easy, but not completely straightforward - it did require some thinking. The word "satellite" immediately made me think of moons, but the fact that "My beginning" refers to more than one letter was unexpected. Things like "what is most common" almost always refers to the letter E in puzzles like this, but finding the word "we" was another non-trivial part. And "the beginning of all things" could have been either A or AT, so we need to think about context (all the clues fitting together) to be sure of the right answer.
