Batman arms the hellspores and issues Darkseid an ultimatum: Release Kara, or he'll let them destroy Apokolips. As Batman was separated from the other heroes, and Darkseid has highly advanced surveillance technology, it is clear nobody else held the means to disarm them. Considering that he refuses to back down even after being severely injured when Darkseid smashes him through a wall, it seems clear that Batman isn't bluffing.
Even Darkseid is impressed with his resolve. After realizing that he's lost, he smiles and says:
Well played. Had the Kryptonian or the Amazon taken that gamble, they would have lost. They do not have the strength of character to destroy an entire planet to achieve success.
But you, a human? You kill your own kind to win battles. An admirable quality. Take the girl. I will make no move against her.
I find it surprising that Batman would resort to such extreme measures. Is there something that I'm missing?