ROCKY: He took his best shot at becoming champ. What shot did you ever take?
Rocky is talking to a lippy bartender here, but he might as well be talking about himself. At this point, he hasn't taken any big shots at being champ, either. He is sticking to the bottom of the barrel.
ROCKY: All I wanted to do out of fighting was prove I was no bum, that I had the stuff to make a good pro.
Although Rocky has his mind on big goals, at this point in his life, he isn't doing anything to achieve them. He needs to back up his big amibitions with big actions.
ROCKY: He says to me "You weren't born with much of a brain, you know, so you better start usin' your body."
Rocky's dad was insulting, but the insult gave Rocky the ambition to be a strong fighter.
ADRIAN: My mother, she said the opposite thing […] She said, "you weren't born with much of a body, so you better develop your brain."
Adrian is shy, but she wants to be smart. Good thing shyness aren't intelligence aren't mutually exclusive.
JERGENS: He picked you, Rocky. Rocky, it's the chance of a lifetime. You can't pass it by.
"Chance of a lifetime" is the key phrase for Rocky, who has been looking for that chance his whole life. Lucky for him that it falls right into his lap.
APOLLO: Look, if history proves one thing American history proves that everybody's got a chance to win.
Apollo is right: America was built on ambition. Rocky's ambition makes him a quintessential American hero.
ROCKY: I guess I'll have to do the best I can.
Doing the best he can will pay off to the tune of $150,000. Rocky's ambition is finally paying dividends.
ADRIAN: Beethoven was deaf. Helen Keller was blind. I think Rocky's got a good chance.
This line shows us how smart she is (Beethoven reference in a boxing movie), and is Adrian's way of complimenting Rocky's fierce personal drive. She believes in him.
GAZZO: You know, you ain't never had any luck, but I think this time Lady Luck may be in your corner.
Gazzo is complimenting Rocky's ambition here. When Mickey later tells Rocky that his opportunity is "freak luck" it's a little different when he says it. Mickey thinks that luck is the only way Rocky is going to get anyway. Both men are right.
MICKEY: They're good fighters, right? They're colorful, they got good records. They fight their guts out for peanuts.
Mickey thinks that ambition comes with sacrifice, and he doesn't think that Rocky has sacrificed enough to be a good fighter. Because of that, Mickey equates Rocky with being lazy instead of ambitious.