Character arcs measure how a character changes or doesn't change.
And it always expresses some point of the story's continuing theme.
I can give you a character right now who is completely flat who doesn't change no matter how many times she gets challenged by Princess Amber, Princess Sofia and Princess Clio.
Princess Hildegarde of the Sofia the First show has never changed she is still the same stubborn want-it-all Princess she was in the beginning show to the very end of it. Unlike many characters who don't change we do get a bit of a back story for her but once the episode happens she instantly slides back into her old ugly ways. She is a flat character that goes through a know-it-all want-it-all negative arc and nothing other characters say make her change her ways does not even bother to listen to her best friend either after she said she would be open to it she goes back on her word there too also.
Tip of this writer's advice is to take the inner personality of your characters and put the one personality that is encompassed with the flaw in the before and the one that has overcome or broken through that flaw in the after slot.
This doesn't mean a character has to completely change into a better version of themselves by the end of your story.
Sometimes you will have a story where your character will be miserable at the beginning and happy at the end.
In Winx Club Season 1 Stella's quite miserable at the being one from dealing with news of her parents divorce and being chased for the sake of her scepter, Stella is technically our protagonist at the start of Season 1 while Bloom quickly becomes a hero's companion of hers, Bloom is miserable too at the beginning of her life but because she wasn't in danger she was helping fight the danger she is not our protagonist she is a side character within the first few episodes of Season 1.
Musa is miserable in Season 1 & 2 and even we all know why, it's obvious.
Only Flora & Tecna aren't the ones miserable.
In Season 2 Aisha and Bloom become both our protagonists
Season 2 Aisha has a flat arc against Darkar meaning she is completely fearless and unafraid of him. This results right out of her refusal to quit.
At the ending Half of Season 2 Bloom does become our protagonist because she's finally in danger whereas the others weren't.
Now There are other storylines that will gives us oh the characters miserable at the beginning and they get to the end almost or maybe completely dying off.
Believe it or not Bloom nearly made it to the worst result twice in Season 1 even as a side character. A Mary Sue/Gary Stu would never stoop down that low because in their character progression there is no character growth or progression. A Mary Sue character is a character who will not change because they're not meant to.
Side characters do need their own arcs.
What are our arcs?
The first arc that nearly all heroes fall into play is the positive change arc.
The Positive Change Arc
A character or characters overcome their flaws and develop strengths in the process.
I'll be honest here Luke has way more than one arc: he has two
Luke: Goes from Self Doubt to Self Acceptance when being accepted into the Rebel Alliance as a great pilot.
Flat arc: he is very selfless in the A New Hope Movie he is constantly ready to do the right thing which if it means convincing Hans to rescue a princess or come back and join a fight to help save people in need that need his skills. He sticks to his gut and says it straight to other people's face this is one of the best things we have ever gotten from Luke in The Original Trilogy of Star Wars.
Enchantix in Season 3 makes all our protagonists goes through a positive change arc of selflessly sacrificing someone because of this you cannot say the Winx afterwards are all zombies because it just doesn't work and it doesn't fall within the theme of Season 3 nor does it follow the Zombie official criteria we've been told time and time again that zombies are created by accidents because of someone not planning ahead for a failed plan in their head: this is the reason why this fan theory sucks and should stay dead, honestly. But those of you who think about that know that I think you are all psycho chaotic nerds with delusional brains and your ideas ruin the real meaning of the Winx Show in Season 3 for real fans of regular stories so keep your mouth shut and especially don't talk to me, because I won't listen to you and your out of this world crazed ideas, because as a Christian I will always prefer a story with selfless sacrifice compared to an accidental sacrifice, Skylights. That is the truth reason why I like Harry Potter Series and the Chronicles of Narnia Series books are full of selfless sacrifice, and same with The Lord of the Rings also filled with selfless sacrifice.
The only other character in the solely movie of A New Hope who had a positive change arc is Han Solo and he's a side character.
His Positive change arc is going from Selfishly greedy to selflessly humanely care for Luke after Luke is being a real friend by challenging Hans' moral by saying. "Well, take care of yourself, Hans, I guess that's what you're best at anyways."
The second arc change for characters is A Negative Change Arc.
Anakin is the best example of this which in turn does actually foreshadow that after awhile one of his own later descendants would fall victim to the same thing he did once. It's not explained as well in the Prequel Trilogy, or The Clone Wars tv show as it in the Kenobi show just by one line of Obi Wan's. "Your need to prove yourself and win a victory is what is blinding you," that is Anakin's true flaw in all of Star Wars, and it is something that Luke gets caught up in later, and we get a glimpse into it in Return of the Jedi from Luke himself.
Anskin from The Movie of the Clones all the way to the end of A New Hope Movie he is always wanting to win to prove he can be the top jedi knight of them all and as the story rolls on he just gets more caught up in any and all of his successes and eventually those lead to trouble even while training his apprentice that was one of Ahoska's flaws too she wasn't trying to be over obsessed with winning some battles but it still happened because it was something her master got obsessed with from time to time so she also learned it.
Then there's our third most flexible arc to work around the Flat Arc
Companions in A New Hope that never change:
R2D2-He's incredibly loyal, C3Po is also loyal yet skittish, and Chewbacca is also loyal those are normal side character hero companions with flat arcs
Leia has a flat arc but it is way more impressive in A NEW Hope than Anywhere else except for the Kenobi show.
Leia has always been incredibly fearless solely within A New Hope movie and that is also because she has this strong spirit of refusal to quit. Leia's never been a quitter and she's quite cool headed even while standing face to face within the face of her enemies.
Obi Wan also has the flat arc treatment because he is a wise and responsible teacher solely not just to Luke in A New Hope but he also manages to teach Han a few things as well, Skylights.
A Flat arc is an arc that contains a main character or a side character that has a strength/strengths or flaw/flaws that don't usually ever change. It has to be one of the other there are not both of these extremes. Thd flat arc cannot have both strength and flaws. Captain Marvel is a flat character with all her strength portrayal that is her sole purpose as a superhero to be physically stronger than the rest this is why yes you can deliberately call her a superhero Mary Sue in that sense she instantly makes me think of Drax I mean come on really she's the female hunan version of him really and I really thought Marvel couldn't sink low enough to rip off their own superheroes.
Musa in Winx Club in Season 1-6 Musa has a Flat Negative Arc. Why is it flat? She never loses an inch of her passive aggressive attitude towards Riven that's why it is a flat arc and it is a negative arc because Musa succumbs to this flaw she keeps using it everyday without trying to fight it off every now and then, Skylights.
How to Do Side Character Arcs Right. . .
Acknowledge side characters take up less screen time/page time compared to the heroes/villains less time to develop them even.
There will be less room growth and far fewer growth beats for your side characters than your main heroes and villains, Skylights.
And Last but not least make sure your side character in some way whether it is said by them in a re enforcing way or not or just said by their stance make sure they fit the big picture theme of your story whether it be a film a or a book.
And the ify rule Story length determines how long your side character arcs will be and how much could be dedicated to them. Pyrix_Fairy