Question

how did the frog become the unrivalled king of the bog again

Answer 1

He killed the nightingale by forcing her to puff her vain and this way he became the unrivalled king

Answer 2

The simple and innocent Nightingale was easily carried into the crafty designs of the cunning frog. He played a trick. He made the Nightingale sing Continuously in bad weather. She was totally exhausted and over trained. One of her Vein got burst and she died. And thus, the frog once again became the king of the bog.