Woundwort leads an army against Hazel's warren and wants to kill or capture all of the rabbits there. Fits the bill, right? But let's note that Woundwort only becomes the antagonist around chapter 30, when Hazel starts to plan the great heist. Which means for the first thirty chapters, we'll need another Big Bad.
Humans and other Elil
From about Chapters 1 to 29, the main danger comes from humans. Humans plan to destroy the Sandleford Warren, a human farmer traps and kills bunnies from Cowslip's warren, and another human farmer shoots Hazel during the Nuthanger Farm raid.
That said, there's also some danger here from other elil, which means "enemies": there are dogs and cats and a badger and birds of prey and… basically, the whole world wants to eat rabbits.