Martin Brody (Roy Scheider)’s Timeline and Summary

Brody gets a call about a missing girl and shortly after discovers Chrissie Watkins' remains.
After assuming he'll close the beaches, he caves to Mayor Vaughn's request to consider it a boating accident and keep the beaches open.
He witnesses Alex Kintner's death by shark, but stays on the beach because of his fear of water.
He meets Quint and Hooper, who'll be hunting for the killer shark.
He and Hooper find Ben Gardner's boat. With a dead Ben inside.
Again, he tries unsuccessfully to convince Vaughn to close the beaches.
He witnesses another gruesome attack, fears for his son's life, and finally gets Vaughn to pay for Quint's services.
He goes out on the Orca with Quint and Hooper and feels powerless and out of place most of the time.
The three of them discover the size and power of the shark.
Brody sees Quint and (he thinks) Hooper get eaten.
In the film's climax, he faces the shark alone in the sinking boat, shows himself to be brave and resourceful, and manages to blow it up.
He finds Hooper alive and they paddle to shore; seems he's cured of his fear of water.