The Navy Revolver is unlocked after solving the Los Santos Slasher mystery and killing the Los Santos Slasher serial killer.
There are five clues left that you have to find to trigger this special event. After finding all the clues, the Slasher will send a message threatening the player. The Slasher will spawn in Blaine County at night (between 7 PM and 5 AM). After killing him, the player will be rewarded with the Navy Revolver and $50,000.