Character is plot. I mean that as, your main character’s arc is (literally) the main plot. Every story revolves around a character (or several)--the point is their journey, how the conflicts they overcome will change them and their world, and their growth as a person.
This also means if your characters aren’t working, the whole thing is going to fall apart. So here's how we learned to create solid characters in screenwriting that also give you an arc (and thus, a plot):
There’s five critical things that go into character building: Goal, Objective, Unconscious Need, Disrupting Characteristic, and a Formative Event.
What your character is physically doing throughout the story. Frodo taking the ring to Mordor is his Objective, Rapunzel going to see the lanterns in Tangled. Mulan protecting her dad by taking his place. Essentially, objective is what we’ve thought of as plot.
The intention behind the objective. Why is your character doing this? This is usually the emotional core of the story, where we tuck away arc and characterization.
Rapunzel wants to see the lanterns to finally get out and start her life. Mulan wants to prove she’s worthy. Your character wants to make someone proud, or hurt someone who’s hurt them, or feel loved. This is the emotion behind their objective and cannot on its own be turned into an arc. One cannot ‘prove themselves worthy’ out of a void, that’s the goal, you also need an objective, ‘prove themselves worthy through taking their father’s place in the war’.
Unconscious meaning your character doesn’t realize it, couldn’t put it into words, and Definitely doesn’t say it out loud. Need, is the start of how to answer this blank space. Your character needs to realize something they haven’t been aware of to achieve their goal. Or they need to realize a flaw in their goal.
For example, a woman wants to run for president (objective) to make her mother proud (goal), but she needs to realize all her mother wants is to spend more time with her, and by using all her time to campaign for president, she’s actually splitting them further apart. Mulan needs to internalize that she doesn't have to be bigger than life to make her parents proud of her and bring them honor.
Your need is character specific, which means no one else should need the same thing. If your need can apply to multiple people, you probably didn’t get specific enough. Everyone needs to be loved, everyone needs to feel cared for. However, not everyone closed themselves off from relationships and needs to open up to people if they want to foster a connection. See the difference?
Disrupting Characteristic
This step is adding a flaw to your character, specifically, it’s the flaw that’s holding them back from meeting their need. If there was nothing holding them back, wouldn’t they be satisfied already?
If they need to see their father as he truly is, maybe their disrupting characteristic is that they’re optimistic to a fault. This characteristic could be a thing the character does (idolizes their father, acts fiercely independent, etc.) or a belief they have about themselves or the world (self conscious, believes humans are inherently cruel, etc.)
The disrupting characteristic is the internal arc your character goes through, they are working and being challenged throughout the story to overcome this characteristic.
This is essentially your beginnings of backstory. The formative event Is the (usually) singular event in a character’s past that made them to be who they are today—importantly, that developed their need and disrupting characteristic.
So, their arc is to overcome their disrupting characteristic in order to realize their need through the conflict they face from their objective. This challenges their overall goal, which was created by their formative event.