The story
The overview of Breaking Bad is the story about Walter White, an overqualified chemistry teacher who also works at a carwash to make ends meet for his pregnant wife and teenage son who has cerebral palsy. Walter is miserable in his life, going day by day until he collapses at his job at the carwash. From there his life takes a turn because he is informed that he has stage 3 cancer, inoperable, and has at most two more years to live. Walter turns to crime using his vast skill set of chemistry to make money for his family when he inevitably dies.
Character study
Walter is a 50-year-old chemistry teacher that also works at a carwash. Walter is a very passive, timid, subdued man who takes things as they come. He once had a promising career in science and chemistry but now is stuck washing the tires of one of his most troublesome high school students. Walter is unfulfilled, just focused on providing for his family. When he discovers he will die soon his life is then filled with a purpose unlike his aimless day by day. He must make enough money to take care of his family when he goes. So, he partners up with Jesse Pinkman, a former deadbeat student of his that now makes and sells heroin. At first Walter is very unsure and scared of what will happen if they are found out. This is shown when they first encounter adversity with local drug dealers and Walter is forced to defend himself by making phosphate gas and kills one of them. Walter's response is human. He is a nervous wreck demonstrated by him throwing up and panicking as he hears sirens in the distance. Over time his humanity, and care for others other than himself decreases as the seasons continue. Walter is told he is recovering and is in remission. This is devastating for him because he committed multiple crimes with the understanding that would die, and everything will go to his family. He would not have to live and take reasonability for his actions. This is another turning point for Walter as he does not want to stop making heroin because he is good at it and makes him feel alive. His purpose now switches again from simply providing for his family to his own interests despite what is best for his family. By the end of the show Walter has made a 360, he is ruthless, cruel, calculating, and is in power.
Scenes
One of the most powerful scenes that shows this character development is the pilot episode and one of the later seasons after he becomes Heisenberg. It contrasts with Walter, his unsure timid self in the MRI, to his later self as Heisenberg, who is ruthless. You can see how scared Walter is in his face in the pilot episode as he fears the worst. But Heisenberg is almost smiling, he is smug because at this point, he still thinks he is going to die and get away with it. He made the best product, a genius among his peers, and is the king of his world.