By the time he arrived

By the time he arrived, there must have been several thousand blowflies in the shop. The archer-fish was having the time of his life, watched by myself inside the shop and fifty or sixty people on the pavement outside.
Could any one please explain the sense of “bold part”?

In other words, the archer fish was having a very good time/enjoying himself.
He was probably feasting on the blowflies, fish relish flies.

to have the time of life’ indicates that someone is having a very enjoyable time.
In this case, the archer-fish was able to attack more blow-flies than he had ever been able to attack before, so the author is comparing him to someone having a great time.