In Octavia's case, her development can be shown in her titles and nicknames. If seasons two through six were skipped over, fans might understand part of Octavia's development. Octavia is in a similar place mentally in the first and last seasons. However, what makes it all the more impressive an arc is everything in the middle. Her journey is not simple, easy, or direct. Octavia drove herself to the edge before understanding where she went wrong and how she could do better.
Murphy doesn't have a variety of names given to him to associate his growth. However, he has one of the best and most noticeable character arcs. Murphy was an angry delinquent when he landed on Earth. Through the seasons, Murphy slowly became less harmful to those around him and became a team player. While Murphy would mainly participate if it meant good things for his own survival, that would change as he experienced more and more.
Octavia: The Girl Under The Floor
Octavia was arrested for being born and sent to Earth as part of the hundred. Octavia is a drastically different person in the first episode than in the finale, which is noticeable in her actions. Octavia is more interested in boys, paying attention to Finn and Atom before meeting Lincoln.
Octavia wanted an identity, and after meeting Lincoln, she started to find it. Octavia did not have much room to grow as a person on the Ark, so landing on the ground was the first step in Octavia's growth.
Murphy: Cockroach
Cockroaches survive everything. Murphy is a prime example of someone who has been pushed repeatedly only to return. Murphy has been hanged, beat up, infected, banished, and sided with the enemy. Murphy made a point to ensure his survival on various occasions.
Murphy makes choices that are not what he would call "a survivor's move in the final season." He may endure everything, but Murphy understands that there is more to life than his own survival.
Octavia: Skairipa
Octavia's opinions and feelings weren't the only parts of her that grew. She also developed into an impressive warrior. Under Indra's training, Octavia gained the name Skairipa, "Death From Above." She worked as an assassin in the fourth season, actively wishing to protect Roan while her friends searched for a solution to Praimfaya. Her fighting skills came in handy many times, and especially during the Conclave.
Octavia merged her fighting skills with her past as the girl under the floor, creatively making hiding spots to survive to the end. After winning, Octavia took it a step further, inviting one-hundred members of each clan to live in the bunker.
Murphy: Emori
Murphy and Emori meet in the dead zone while traveling to find the City of Light. A few months later, they meet again and work together. Both live under the desire to survive, so they start to rely on each other. Their relationship brings out a new side in Murphy.
Emori is the first person Murphy shows to genuinely care about. As time goes on, they grow closer and look out for each other's survival. Murphy would rather die spending time with Emori in his mind than live without her, explaining that without Emori, Murphy would just be surviving, not living.
Octavia: Blodreina
Love it or hate it, Octavia's redemption arc wouldn't be nearly as exciting or satisfying without Blodreina. Blodreina was the worst of Octavia, the culmination of desperation and desire. Octavia transformed into a terrifying leader who was willing to do anything for Eden.
Octavia's darkest choices are wrapped up in Blodreina and what she did to ensure Wonkru's survival. This certainly wasn't the high point in Octavia's life, but without these experiences, she could not deeply understand that the best answer to the last war is not to fight it.
Murphy: Friendships
Two of Murphy's most prominent friendships in later seasons are with Bellamy and Raven. After the six-year time jump, Bellamy makes it part of his mission to make sure Murphy understands that he isn't worthless.
In season seven, Murphy is confused and upset to learn of Bellamy's death. He is also close to Raven, and their friendship is a significant part of the last three seasons. Their friendships helped Murphy care for more people than just himself and Emori, and he looks at them as family.
Octavia: Aunty O
Octavia's redemption begins on Sky Ring. While Octavia returns from the Anomaly in season six with the determination to save innocent lives, the truth as to what happened to her is not shown until season seven. Octavia spent ten years with only Diyoza and Hope.
While on Sky Ring, Octavia tried to get back to Sanctum but failed on each attempt. Octavia bonded with Hope and Diyoza, gaining a new family as the only three people on the planet. So much time in a peaceful environment gave Octavia time to move forward from her past and give her a new perspective.
Murphy: Protecting Children
With all his friends gone, Murphy is in charge of Sanctum. Along with Emori and Indra, the three work to protect the innocent Sanctum citizens from the angry Prime believers, Children of Gabriel, and Sheidheda. This is a vast difference from who Murphy was in season one.
In the early days on the ground, Murphy leads an angry search against Charlotte. Driven by guilt and horror for her own actions, Charlotte wanted to turn herself in, but in the end, things ended horribly for everyone. Charlotte committed suicide, and Murphy was banished. In season seven, Murphy devotes time to protecting the innocent children and helping Madi get through a panic attack.
Octavia: Savior Of The Human Race
The human race is being tested, and Clarke Griffin has failed. However, it isn't over yet. Raven begs for humanity to have more time to change and become better. When the Being of Light brings Raven to the battlefield to prove humanity won't break the violence cycle, Octavia Blake saves the day.
Stopping the fighting, Octavia steps up, asking her people and the Disciples to stop fighting and recognize that they are all that is left of the human race. Octavia makes it known that fighting and killing is not the way to win, but it is how everyone loses. A grand arc for an epic character, Octavia Blake, is responsible for the human race transcending.
Murphy: Hero
Who would have thought back in season one that Murphy would become a hero? Yet, that is where his arc takes him. Murphy slowly understands that life is about more than just surviving.
When Clarke destroys the Disciple's helmet, Murphy desperately wants it fixed to save everyone on Sanctum and bring them to Earth. Murphy is left to run things in Sanctum, and while he doesn't make any large moves against Sheidheda, he does protect as many people as he can while he waits for his friends to return.