Through my studies of narrative, I've learned that a protagonist is not necessarily the main character or the hero. Don Quixote is the main character, but Sancho Panza is the protagonist. A protagonist is the person who changes as a result of the story. The protagonist enters the story because of conflict with the antagonist. The protagonist is supposed to be the person the audience mostly identifies with.
There are many different kinds. The hero protagonist is the most basic, most common. This is when the protagonist and the force for good in the universe is the same character. They're sympathetic because they're who we want to be, not who we are. Supporting protagonists are usually the POV character, but not the hero. Examples are Red from The Shawshank Redemption, Watson from Sherlock Holmes, and Mary Poppins. A Pinball Protagonist is simply bounced around from one situation to the other. Always reactive, never proactive. Forrest Gump, Charlie Bucket, and Bilbo Baggins tend to this type. Sometimes a protagonist doesn't win, or dies right away, maybe as a decoy (like in Psycho), and other horror movies.
That means Darth Vader is the true protagonist of Star Wars. He's the one that changes the most. True, Luke Skywalker does go from farm boy to uber-ninja, but Darth goes from noble warrior to dark lord and then redeems himself. In The Dark Knight, the Joker is not Bruce Wayne's antagonist. It's Harvey Dent. How can you tell? Because Harvey Dent is the one getting in the way of what Bruce Wayne wants. Bruce wants to stop being Batman. Harvey's got the skills to do it, but he needs to step up. That's why those incidents like Harvey torturing the fake cop for information are so devastating to Wayne. That's why, in the ending, Batman is facing Two-Face, not Joker.
So now that those terms are defined, who is the protagonist of The Little Mermaid? Well it's clear that Ariel is our main character and hero. She's the force for true love in the world. For pursuit of knowledge and acceptance and curiosity. She has agency -- she makes the decisions that affect the plot events. She's the one who wants something. She's the one who overcomes obstacles. But is she the one that changes? Some say no, some say yes.
We know Triton definitely changes. He goes from hating humans to letting his daughter marry one. From staying isolationist under the sea, bigoted and unsympathetic, to letting their two worlds interact (I always wondered if the existence of mermaids becomes a "thing" after TLM). After Ursula blows up, Triton should be one happy camper. His primary threat to the throne is gone, his daughter's back. It's pretty much back to status quo. Nevertheless, he realizes how wrong he was, and grants her wish to be human, so she can
But how does Ariel change? Does Ariel ever stop wanting the thing she wants? From the time she sets on eyes on him, she never stops loving Prince Eric. She never stops chasing her dream of staying human. She never turns from her goal, she never gives up (except for that small part where she's crying on the dock, but who wouldn't be doing that). Modern criticism says that Ariel is simply a ball in Triton and Ursula's court.
Or is she? There's one small part where, when Ursula is dragging her back down into the depths, Triton confronts her. As Ursula shows him the contract, the eels hold Ariel back as she says "Daddy, I'm sorry, I- I didn't mean to..." That would indicate regret -- a look back at where events led and the realization that this may not have been worth it. It's just a blip, barely a few shots, but it seems to indicate that she's learned something. So where does that leave us? Is she a changed person? Is she as stubborn as when we got into this whole mess?
Maybe Ariel is a deuteragonist. That's always a hard one to define. It's not a sidekick or a supporting protagonist (neither Triton or Ariel are assisting each other or following each other around). Not a decoy protagonist, since both are in the movie for the length, and it doesn't end in a bait-and-switch. The deuteragonist has his/her own story, own character arc. Definition-wise, he/she is simply the second most important person in the story.
Triton and Ariel revolve around each other. Each is doing something the other doesn't like, and that causes conflict. Both have flaws, both make sacrifices to get what they want. Triton may not be the protagonist, but he is definitely Ariel's antagonist. Not Ursula. And in the end, neither are in the same place they were before. Much like Lady & the Tramp or Frozen. It's Lady's story, but Tramp is the one that changes. Lady never wavers from her belief that a good home in exchange for servile guardianship is better than freedom & risk. In Frozen, both girls change. Anna learns not to jump headlong into situations. Elsa learns the consequences of rejecting love.
I think this question all depends on one thing -- what is Ariel thinking when she's on that rock?
She's up there, gazing at her prince. Is she saying goodbye? Or is she contemplating a new way to get legs? Is she unchanged? Is she giving one last look before diving back under the depths, never to return? Have the choices and obstacles she faced changed her?
We may never know. The writers didn't even give her a line after Ursula is dead. I guess they left that mystery up to us, to forever ponder.