There are plenty of examples that you could point to in order to demonstrate how Pip actually becomes a true gentleman through the tragedy that he experiences in the novel. You might want to think about how he comes to treat Magwitch like a father, or when he faces Miss Havisham for the last time. However, one of the defining moments of the novel for me is when Pip goes to propose to Biddy only to discover that Joe has got there before him, and already married her. Note how he responds to this rather unexpected shock:
"Dear Biddy," said I, "you have the best husband in the whole world, and if you could have seen him by my bed you would have--But no, you couldn't love him better than you do."
Such a gracious comment shows exactly how far Pip has grown up and matured. So many comments in the novel that he makes to Biddy before show his complete lack of self-knowledge and understanding. Finally we are beginning to see that Pip is growing up and becoming the gentleman at long last. His graciousness in responding to the destruction of his marriage plans with love rather than any other emotion proves this.