Pyrrha Nikos

Unlike what the writers wanted the audience to believe, pyrrha was never the strongest fighter in the school (let alone her class) and i actually found her to be one of the weaker fighters, especially comparing her to nora who's actually shown to be the one carrying the entire team. it would've been a lot better if this was intentional, if that pyrrha's character arc was her being nowhere near as good as her reputation made her as, where she decided to join beacon to get as strong as what other people think she is, but that's just guess work on my part, it's not even getting into the plot grand canyon that is *why* she's supposidly, which is so nonsensical that i won't be able to go over every problem with it. the main problem of this plot hole is that there is no way she could be able to keep her semblance a secret for so long, especially when we are our introduced to this semblance by her telling two people she barely knows about it. not to mention that it's nowhere near as much of an advantage as the writers/fans try to make it out to be, there are so many scenarios that involve fighting without metal involve, even in a ridiculous setting like rwby, that it's not even funny. but i'm getting off track, this could easily be explained away as *some* of her tournament opponents being bribed to take a fall by her parents or couch or whatever and her reputation is more for publicity sake, this is just me trying to fix the broken mess that is this story.
Pyrrha's motivation never made any sense, to the point that any cliche backstory would've been better. for example, she could've become a huntress because her mother is sick and they need the money to keep their house. this would give pyrrha an actual motivation that gives her her own autonomy rather than being a trophy waifu for jaune. you can even say that beacon pays better than haven, which is why pyrrha is in beacon specifically.
Pyrrha's death was forced, stupid, gratuitous, and unnecessary. The fact that Ruby shows up at the second of her execution, Ren and Nora don't even mention her throughout volumes 4 and 5, Jaune's motivations flip flop between safeguarding his friends and getting revenge, and we don't even get a glimpse of her past when they come to Mistral just shows how contrived her death was.
Her character revolved around finding love with Jaune, the only person to not treat her like a celebrity, but she chooses to "follow destiny" despite she's known Jaune for a year and Ozpin drops this on her just a few days prior BECAUSE of her celebrity status.
Ozpin's the one who hyped up these powers AND he's a teacher, so why would a STUDENT with no maiden powers think she stood even a lick of a chance against someone WITH maiden powers who defeated the teacher? If Pyrrha was arrogant or an idiot in the previous volumes, it could've worked, but that wasn't the case.
The fact that there are people agreeing with you and you're writing as well scares me for what will pass for good writing from now on.
TL;DR. I understand I sound like someone who knows all the right answers, and I know I don't, but this is the worst death scene I've ever seen and I'm not changing my mind on that.
In the end, when Jaune is Pyrrha’s only fleshed out relationship, it feels like she was just a prop for Jaune’s hero journey. Even if they always planned to kill her they could have set it up and done it in a way that doesn’t feel like the writers are just setting up for yet another Jaune story arc.
I also don't really like the whole Pyrrha’s closest friends putting her on a pedestal despite her hating that. Seems counter to her character for the sake of feels.
(...)
Like much of Pyrrha’s arc to me, it feels like a case of trying to smooth a narrative into place that wasn't really there at the time and using emotional peaks to distract from the lack of actual substance.
We don't like Pyrrha's death because it just felt out of character and kind of forced. Like, in the first 2 volumes, we see she's an exceptional fighter but actually wants friends just as much as becoming a huntress. Then she's given an ultimatum: become a maiden, thus saving the world but at the expense of friends and love, or say no and stay with your friends at the expense of leaving the world as a much more dangerous place. It's great drama...and then Cinder kills Ozpin and takes the powers for herself. It was obvious she couldn't beat Cinder, and Pyrrha ran away from the scorpion grimm during the emerald forest trials until her team and RWBY were all together so running away is in character with her. As for the whole "Destiny" defense, Ozpin's the one that brought it up only to tell Pyrrha and Jaune to go get help from the other adults. When she sends Jaune away and goes to fight Cinder by herself, she just looks like a moron, especially if she thought she had a chance at beating Cinder since, again, she's a student and Cinder killed Ozpin who was a headmaster. Couple all of this with Ruby conveniently showing up a second too late and activating her eyes and kicking Cinder's ass, it makes the whole ordeal feel like a plot contrivance, despite whether or not that was the intent. TL;DR Essentially, people who hate Pyrrha's death hate it because it doesn't line up with the character we had when Monty was alive, and it shows. In Monty's version, Jaune being the cause of her death (presumably because he was always clumsy and one to get in the way) kind of seems in character, especially because Achilles (whom Pyrrha's based off of) was killed by Paris who was much weaker than Achilles and Jaune was always one to do stuff before thinking it through. It just felt more in character for both of them. What we got didn't feel in character at all with Pyrrha, and it was so obvious she was going to die. People say "she believed it was her destiny to fight Cinder" but this means she put the whole destiny belief over common sense and made a choice without thinking of consequences (she's a celebrity, so how come no one seemed scared that "the invincible girl" died? She was on cereal boxes for God's sake, are there no children who would be sad that their role model died in battle? Wouldn't this mean more grimm attacks, creating more tension to the plot?!).
In a nutshell, it just feels out-of-character to me and they could've done more with her character. I don't get angry at people who disagree, so if you're fine with how her death was handled, okay, but I'm not. Hell, I have friends in real life who saw it for themselves and their responses were "yeah, it just felt so random."
Also, Hazel doesn't use metal to fight and it would've been cool to see a villain with an earth bending semblance and can put Pyrrha to shame. You shouldn't create tension by weakening your heroes but strengthening your villains. If Miles and Kerry wrote MHA, All-Might would've died in the final battle of the first season and all the villains would be 1-dimensional killers with nonsensical motivations.

The problem with Pyrrha is pretty much encaptsulated in this DBZ Abridged scene but replace Trunks with Pyrrha, "Please love me dad" to "please love me Jaune", and replace Android #16 for Penny.

Physical Description

Specialized Equipment

Pyrrha can only manipulate metals lighter than her own weight and going further than that stresses her muscles. [https://yt3.ggpht.com/26FaKx-s0UwN9-aB43sYnjuVZXyHVdwGiP7sP6DjUiZAMbNuJ33YQGj27U7cb_od4IpwF_hsM4zqZg=s443-nd-rwa] Chinese mobile game animation for Pyrrha’s weapon fighting style.

Mental characteristics

Personal history

We don’t know Ren and Nora’s goal because Miles and Kerry focused all their time trying to develop Jaune rather than characters people were actually interested in. 
Jaune’s development should have ended with him dying. It should have ended with him no longer being the “lovable idiot stuck in the tree” that he wanted so badly not to be. His development should have ended with him becoming a martyr in the place of Pyrrha, thus giving everyone else so much more opportunity to be developed.
The only people who have been shown to actually react to Pyrrhas death are Jaune and Ruby which is a load of bullshit considering Ren and Nora were her friends too. Don't worry, I'm sure that Jaune will eventually burn to crisp a la the JNPR death theory :^).
Anyhow I dislike Pyrrah's death since they killed her when she was just starting to get interesting. I don't think Jaune's death would have been right either though because his character development was half baked. IMO the show wasn't developed enough to pull a stunt like this. The first three volumes timeframe is analogous to a standard 26-episode season. Maybe I think this way because like you said I watched them all in two weeks instead of three years, but honestly not much happens. And they also wasted half of volume 3 on gratuitous battles in the arena that did little to advance the plot or characters.
And yeah Ren and Nora honestly came across as seriously lacking empathy.
The sad part is Pyrrha had no reason to die in the plot her and Jaune could have both lived but Pyrrha went all like: I have to fight this all powerful fire woman who killed arguably one of the most powerful if not the most powerful huntsman on Remnant for reasons... It was one of the most stupidly written character deaths I have had the displeasure of witnessing simply because there was no real narrative reason for it to happen. Oh yeah. Honestly the entirety of Vol 3 contrived itself to kill Pyrrha. Beacon fell, the tower fell, so why didn't they gather their forces to fight Cinder like Ozpin said? Qrow, Glynda, Ironwood, and everyone else is fighting there so it wouldn't be hard. Or they could have retreated since they had such a hard loss. The fall of Beacon was depressing enough there's no need to kill anyone.
Disagree, Phyrra rarely developed any significant relationship outside of Jaune, sure she may have talked to Ren and Nora for bit but it never really went further than roommates, heck Ren and Nora don't seem bothered about Phyrra's death, they don't even have a scene were they grieve. Phyrra only had her struggle of being put on a pedestal but that was only mentioned once and it was to serve Jaune. Her struggle with the maidens powers could of been awesome, but the writers killed her off before they could do anything with it, her dying was an mistake there was way more they could of done with her, but they got rid off her to serve Ruby's silver eyes, which was pretty meaningless in the end.

Accomplishments & Achievements

Heck, Pyrrha is FROM Mistral, isn't she? But she chose to go to Beacon. We could be seeing people touting her as a martyr and her name being used to further political or business agendas, showcasing the very thing she hated about being a celebrity. We could have JNR meeting Pyrrha's family and maybe have some of them loving the fame association while others are disgusted by it.
Phyrra developed? She was an character that existed to serve Jaune arc and nothing more, we got little details about her but they were never explored, even her destiny BS come out of nowhere and before they could take it somewhere they killed her, she was plain wish fulfilment for the fans that put themselves onto Jaune nothing more.

Personality Characteristics

Motivation

Our history is replete with examples of natural disasters eradicating cities or civilizations. Such a history actually fits in with the sea-faring Greek kingdom comparison earlier. A notable case is the Minoan eruption, which is believed to have prompted the downfall of that Greek island's civilization and its subsequent invasion by another Greek power. Most likely the area was a major trading city with it likely being a prominent point of trade with Vacuo and Vale. Back then there were probably even large areas to the south, north, and east, that had as few Grimm as the western side of the inland sea. Several volcanic eruptions later and the entire area was depopulated of humans. With the loss of this city, the other regions nearby quickly fell to the Grimm. Although many undoubtedly were killed in the disaster, many can be assumed to have been evacuated across the inland sea to the western bay city, causing it to grow even more as it absorbed the growing refugee population.
This continent is the other prime location for the Mistral region. Since we have established the other three kingdoms in Remnant: The Game, the fourth kingdom must be the one played by Yang. In that case, one has to consider the possibility that "Mistral Trade Route" was not a region she controlled, but instead one of the kingdom-based cards she played. Pyrrha's Greek inspiration goes along nicely with the possibility of Mistral being in this fourth kingdom.
Such a prospect does raise the question of Sanctum's location again, but that depends on the exact location of Mistral on the continent. It is likely that human settlements exist all over the continent given the seafaring nature of the kingdom. Were Pyrrha from one of the southern areas, it might have been just as viable for her to study at an academy in Vacuo as one in her own kingdom. Since students travel across the continents to attend Beacon there is no reason the same cannot happen in lower-level education. As to her taking part in the Mistral Regional Tournament, it would not be unreasonable for her to participate in a tournament back home while attending school in another kingdom. While it is possible Sanctum and Haven are in the area of this fourth kingdom it only raises further issues with Sun's stowaway act.
A different tantalizing idea regarding Pyrrha also emerges if one assumes she is from this fourth kingdom. It has been suggested at times that Pyrrha is an orphan. I am personally not big on the concept, but the calamity mentioned above would provide an intriguing backstory. Part of Pyrrha's background could include her being a survivor of this tragedy when she was just a child and being taken in by adoptive parents. Her survival could even play into the description of her as the "invincible girl" if she avoided harm during the tragedy in some miraculous fashion.
I'd like to add something to the Pyrrha theory, if I may. A 'Pyrrhic Victory' is, by definition, "A victory with such a devastating cost that it is tantamount to defeat". While the survival by Pyrrha and the rest of the Kingdom can be considered a 'Victory', the theory presented here suggests it would come at such a heavy cost (E.G loss of life and land) that the end result is barely salvageable. It could also give Pyrrha a motivation for becoming a huntress- she wants to save her people and retake her homeland.

Savvies & Ineptitudes

Jaune has been teaching Pyrrha how to cook, more than once she has burned their eyebrows off.

Likes & Dislikes

Pyrrha loves chocolate, she'll never get it for herself but taking it away from her is like taking a stake away from a wolf.

Personality Quirks

Pyrrha sleeps like a slob, limbs scattered every which way and halfway off the bed, blanket only half covering her, and worst of all, she drools.

Honorary & Occupational Titles

Pyrrha being a celebrity doesn’t mesh with the idea I have for how Hunters affect society, so change Pyrrha’s character arc to be about something else. Besides, we already have Weiss if you want the “celebrity put on a pedestal but it makes them “lonely at the top” character arc.

Birthplace

the Eastern-inspired Mistral; the home to the VERY Greek Pyrrha.

Character Prototype

The Iliad is the oldest known example of how to write a war story so Pyrrha should have a lot of depth when it comes to dealing with this topic. pyrrha has a fake public persona that is akin to achilles with her actual personality being that of the show. As for what you said about Achilles; Pyrrha being a representation of him wasn't a bad idea, but I think you misunderstood the symbolism behind his death. Achilles's death was at the hands of Paris who was also a complete weakling. Paris shot an arrow at his heel, HIS ONLY WEAKSPOT, and Achilles died. Morale of the story: No matter how strong an opponent is, there's always a weak point that even the weakest man can take advantage of. If the "arrow" between her boobs was what was meant to be "Symbolic" then it fails at representing the Greek hero.