I want to put a disclaimer here saying that I am by no means a game designer. My suggestions are merely what I think could be fun and/or interesting and what may fit Valkyr's thematic/gameplay style.
VALKYR - WHY HER CURRENT KIT DOESN'T WORK -
Overall, with Valkyr's design thematic being based on rage/brutality, there's really only two abilities that fit that thematic, those being Warcry and Hysteria, but even then, those abilities have issues on their own. Let's start by listing these abilities off in order and talking about why they don't work for her thematic.
Passive - Knockdown recovery and immunity to hard landings is severely underwhelming, nor does it fit her thematic because it doesn't quite say "rage" to me, but moreso fits someone who is moreso nimble/agile/quick on their feet. Rage to me can be described as unstoppable, so were her passive to be preserved, I'd honestly just say that she should be immune to knockdowns as a whole, along with being immune to hard landings, but that won't be the case, as will be described later.
Ripline - Ah, yes, a relic from the old days of Warframe, back when mobility was spinning around really fast. Nowadays, what ripline used to function for can be done by basically every frame, even those without any form of mobility boost. This ability would more than likely need to be rebuilt from the ground up to be even remotely useful.
Warcry - While boosting you and your teammates attack speed is a good way to display "rage," there's a lot more that could be done with this ability to display that thematic better, as will be described later on as well.
Paralysis - Another relic of old times, Paralysis has become severely underwhelming because it's barely even a crowd-control ability. This would more than likely need to be overhauled or replaced entirely.
Hysteria - In it's current state, Hysteria has a very good baseline for her thematic. While being invulnerable is a very powerful tool, it uses up too much of the ability's power-budget to be worthwhile when compared to many of the other exalted weapons in the game.
To me, Valkyr is a one-woman army of rage and power. She should be able to take on hordes of enemies and after they're all dead, she should be able to come out of that fight even stronger than before. As a one-woman army, her playstyle would be a lot more selfish than before, allowing more of her power budget to be aimed at making her better at one thing - Ripping enemies apart like stuffed animals.
POTENTIAL CHANGES -
Passive - Valkyr does not use her Parazon to do mercy kills. Instead, she uses her claws. Upon successfully landing a mercy kill, she gains a damage/speed buff for a duration, which can stack a few times. Her mercy kills still activate Parazon mods when applicable.
This would potentially call for custom mercy kill animations, but I think that would be good for her overall, since her animations could be much faster than other frames when they do mercy kills, allowing her to incentivize going for mercy kills to proc her passive. This also incentivizes her going into the thick of a fight, exactly where she wants to be.
1 - Ripper - Valkyr targets the nearest enemy under a certain health threshold and dashes to them, ripping them apart with her claws and executing them. Any enemies executed by this ability proc her passive.
Since Ripline can basically be outright replaced, this is what I came up with. Giving her a tool to more readily proc her passive will allow her to more effectively push through enemies and allow her to keep her buffs up.
2 - Warcry - Valkyr gains attack speed and lifesteal for a duration. Any enemies that are executed/mercy killed while this buff is active heal her to full health.
This is where the one-woman army comes in - Instead of buffing her allies, Valkyr will now only buff herself, allowing the buff to be more powerful on it's own since it only affects her.
3 - Paralyzing Scream - Valkyr lets out a terrifying scream, causing nearby enemies to become paralyzed with fear. Enemies that are paralyzed by this ability have their execution threshold increased.
This is a tool for a bit of safety. If Valkyr becomes overwhelmed, this would allow her to have some breathing room to get back to doing what she wants to do.
4 - Hysteric Rage - Valkyr gains damage reduction, becomes immune to knockdowns and readies her claws. Enemies that are killed by her claws proc her passive, and her passive stack cap is now doubled.
Hysteria on it's own is really only used as a tool for survivability, and I think these changes allow for this ability to become more than just a tool to stay alive. Giving her incentive to actively kill enemies while the ability is active allows her to become a snowballing death machine capable of bringing down the toughest of enemies like they were nothing.
IN CONCLUSION -
Valkyr hasn't aged well at all, and she could desperately use some love and care to push her up to being what she is meant to be - A one-woman army of rage and bloodshed. These changes in my eyes allow for her to become that.
If you have any feedback/opinions to give, please keep it constructive. Thank you.