So apparently to upgrade my Barbarian Armor in BotW I need to kill Lynels who are the real hardest class of creatures in the game to kill, with the silver manes being the highest color palette swap. They seem deadly but they suck so bad in melee it's mostly a deal of "do you have enough durability to deal 3,000 damage"?. Heck, you don't even have to dodge their charge attacks, Stasis+ gives you free hits and they are auto-stunned immediately following that giving you a nice time saving heavy arms spin for some rapid damage. And their slightly faster triple swing allows even mistimed back flips to trigger a flurry.
I think upgrading the barbarian armor is going to be the easiest set to upgrade in the game so far.
5000 damage for the Silver Ones
You get free-hits while they're on their back. It takes no durability off of the weapon.
The optimal strategy to farm Lynels, as far as i am aware:
After you spot the Lynel, approach and, before he notices and starts his charge/pull out his bow, use Revali's Gale to get a lot of height, and use your best bow to pummel the shit out of the Lynel with Shock Arrows while you descend.
If you play your cards right, he'll stun, and you'll be able to land next to him and mount him. While still descending, switch to your best weapon and mount and beat him senseless until he bucks you off. Get clear of him, and use Revali's Gale again, pummeling with arrows. Stun, mount, repeat.
If done right, you'll only use the durability of the bow, not the weapon, and you SHOULD be able to kill him with the three uses of Revali's Gale.
Higher level Lynels always drop at least 10 shock/frost/fire arrows and a bow, so it's not like you're losing out by going with this strategy. And you can always use regular arrows, they deal less damage, but much easier to come by.
If you somehow didn't manage to drop the Lynel with the 3 uses of Revali's Gale, not all is lost.
Use the Master Sword, as it is effectively unbreakable. It's a bit harder to get the dodge timing for Flurry Rushes on the Lynels, but it's pretty doable. The Charge is the easiest one to get the timing for, while the spin to win is the hardest. Try and get flurry rushes whenever possible, but if not, Stasis+ will make short work of the Lynel.
By following these simple steps, farming Lynels should become as easy and pain-free as it can be. It often takes more than the 10 minutes for the Master Sword + Revali's Gale to recharge for you to get to the next Lynel, so you can continuously farm end-level gear from them without expending much or any of your resources or having downtime to go to town and buy more gear. You don't even need to heal most of the time.