How does Percy show that he’s a hero in chapter 17 of The Lightning Thief?
Stereotypical heroes are brave and try to save people. Percy does both in chapter 17. Immediately upon entering the water, a mako shark closes in on Percy. Instead of freaking out at the sight of an approaching shark, Percy grabs its fin. That's brave. I would never attempt such a thing, that's for sure.
As for saving people, Percy saves his friends at the very end of the chapter. He attempted to protect his friends earlier against the knife wielding kids, but failed. Nevertheless it shows his bravery and attempts to save others. But at the end of the chapter, Percy most definitely does save his friends. They have unwittingly been captured by Crusty, and Percy tricks Crusty into being tied up by his own trap. Percy quickly seizes the opportunity to save his friends.
I would like to mention one last heroic detail about chapter 17. Generally speaking, a hero will go through a 10-12 step heroic cycle. At one point in that cycle, the hero is helped/mentored by someone with extra, special knowledge of some kind. That occurs when Percy meets Nereid. She not only gives him advice, but she gives him special hero weaponry. She gives Percy three pearls.
"take these, and when you are in need, smash a pearl at your feet"
It's no different in concept than Obi-wan giving Luke his light saber or Thor finally obtaining Mjolnir.
In chapter seventeen, Percy, Annabeth, and Grover leave Las Vegas and go to Los Angeles. The taxi they took from Las Vegas drops them off at the beach in Santa Monica; Percy then goes into the water and speaks to a Nereid (a spirit of the sea and a helper of Poseidon), who gives him three pearls and some advice about following his heart. After that, the three friends end up in a shop called Crusty's Water Bed Palace, which is run by Crusty, aka Procrustes 'The Stretcher' who was one of the giants Theseus encountered. Crusty trapped Grover and Annabeth in two of his beds and started to stretch them to fit the six-foot length of the bed (that was his M.O.). Percy shows his heroism by trapping Crusty in one of his own beds and freeing his friends.