God of War

The first 8 Valkyrie fights are not particularly tough. Eir was the only one that gave me any kind of challenge, but she was also the first one I fought. Pay attention to the move set and learn to dodge and parry at the right times. Dodging is prominent in all the fights.

The ninth fight, the Valkyrie queen Sigrun, is a substantial step up in difficulty and the hardest fight in the game in my opinion. It was the only one that required trying many, many times.

Prep for the fight:

1. Take the time to grind out the resources to level up to level 9 gear. The difference in difficulty for attempts at level 8 and 9 was substantial. At level 9 her attacks are damaging, but not devastating, and you do substantially more damage to her. I saw a lot of advice on different builds, but the thing that I found, by far, the most effective was getting to level 9. Fighting her at level 8 I was making it to halfway through her health bar, but once I was level 9 I would consistently almost beat her and only needed a handful more attempts to beat her Max out the levels on the gear you use as much as possible. I would recommend using the deadly mist armor. You should get enough resources to make it and upgrade it grinding for the Niflheim trophy.
2. Have enhancements in to reduce blind damage by the 85% max. Her hardest attack to dodge is physical, but beyond that the ones that gave me trouble dealt blind damage. The reduced blind damage made a substantial difference in overall damage taken.
3. Use the Mistbourne pommel for the axe for the health recovery (and pommel of choice for the blades), Atreus' legendary runic attack for health recovery, the wolf runic attack for Atreus, Tyr's Revenge and River of Knives for the Axe, Gift of Apollo (and preferred light runic attack) for the blades, the Shattered Gauntlet of the Ages (fully upgraded this allows for three enhancements to get to level 9), and a legendary resurrection stone.
4. Max out your health and rage meters with upgrades (which you should have already done if you're going for the platinum) and have full rage and health to start the fight.

Fighting Sigrun:

There are plenty of lists out there that go over her list of attacks, so I won't list them all here, but will cover what I found to be the best openings to attack and how to recover health.

1. Rage: When your health gets down to about halfway Spartan Rage and attack. This will have the benefit of increasing your health and reducing hers. It's also the reason for the legendary resurrection stone. Upon resurrection immediately Spartan Rage and you should be able to get most of your health back and further reduce her health.
2. When she lifts into the air: Use your leviathan axe for a ranged attack. This will stun and knock her down. This will give you an opening to attack her. I found taking the time to recall my axe wasted too much of the window so I went in with fists.
3. When she hides behind her wings: Activate Gift of Apollo (if charged) first, activate the wolf runic attack second, use your other blade runic attack third then attack with your blades as much as you can before she recovers. The wolves will give you a few second window to attack and recover health via Gift of Apollo which can regain a nice chunk.
4. When she does her ice attack: Dodge to one side while the initial stream of crystals is coming out, and then when there's a gap dodge to the other side to avoid the large blast.
5. When she jumps into the sky: immediately dodge anywhere. Just out of the way. Half the time this is only one jump, half the time it's three. Always treat it like it's three. Dodge two more times immediately following the initial dodge.
6. If you crush a health orb near her it will stun her for a moment. Use this opportunity to use an axe runic attack. River of Knives is more effective if you catch her stunned. Tyr's Revenge provides some stun so you can attack her with fists while it's hitting, but I also found it difficult to always hit her.
7. If she jumps into the air for a swoop attack: lock on, dodge to one side, follow her path behind you if possible, dodge to the other side when she comes back, and during the third pass dodge back to the original side. It's an easy attack to dodge, but does decent damage if you don't.
8. Using the Shattered Gauntlet of Ages, if she is near, will open up a brief stun window to do an axe runic attack.

Do not simply run in and try to fight her toe to toe. Be patient, look for and create openings. Recouping health helps a lot. Learn her moves.

1) Drop difficulty to easy
2) Equip resurrection stone
3) Use a moderate to high Cooldown build
4) Keep shield up
5) Always evade to the right
6) Use ALL Runic attacks at every opportunity
.....I'm defeating every Valkyrie on my first or second attempt like this....

There are 8 Valkyrie that you need to slay before being able to challenge #9; the Valkyrie Queen. There's 4 in Midgard, 1 in Alfheim, 1 in Helheim, 1 in Muspelheim, and 1 in Niflheim

They are tough, but not impossible. Make sure you keep your shield up, parry if you are confident about your timing or dodge as many attacks as you can. Whenever one goes into the air, have Atreus fire some shock arrows or throw your axe at them to get them on the ground and stun them. Make use of the summons and rune attacks whenever you can. Keep a Resurrection Stone handy in case things get bad, and remember to breathe if you get frustrated.

If you vote negatively, please leave a comment on how I can do better

For better visualization, here's a guide by PowerPyx: