I got these references from Nyrhex on another thread: "What country had the largest navy in history?"
The Egyptians did a fair job of fighting off the Sea People ... but it was near & in the delta ... not exactly sea battles.
The second Ptolemaic Pharaoh (Ptolemy II) did a fair job with their navy:
"In what has been described as an ancient naval arms race, the successors of Alexander produced the largest warships of antiquity, some as long as 400 feet carrying as many as 4000 rowers and 3000 marines. Vast, impressive, and elaborate, these warships "of larger form"--as described by Livy--were built not just to simply convey power but to secure specific strategic objectives. When these particular factors disappeared, this "Macedonian" model of naval power also faded away--that is, until Cleopatra and Mark Antony made one brief, extravagant attempt to reestablish it, an endeavor Octavian put an end to once and for all at the battle of Actium. " The Age of Titans
"One calculation suggests he had 4,000 ships in service, though the effective warship strength was probably a tenth of that." Grainger, Ptolemaic Egypt
---I'm guessing the 4000 number includes mainly Nile river boats, and that the Mediterranean fleet is rolled into this.
The best navies were all from the Mediterranean, particularly in the eastern basin. The Mediterranean was the undisputed world sea where shipping came of age, the rest of the ancient world was a total backwater.