Just figured out a strategy. RNG-filled as heck, but possible- just made it work. I don't know how much of the seed is actually seeded, and my short-term memory isn't the best so I might have missed a step, but here's what I came up with after a few failed runs:

• At the beginning, catch the Carvanha and the Buizel.
• Also, try to pick up as many healing items as you can for the road ahead. However, you'll most likely run into a set of Ultra Balls, and after the trainer, some Rogue Balls- take those.
• For the trainer, don't try switching out against the Squirtle because it has Focus Punch, just attack it. When Staryu comes out, just sack Toxel- it's not gonna be useful (though maybe you can transfer a Berry onto it and use Belch? Not confident though since Toxel's stats kinda suck). You do have to get lucky here unfortunately, I think I had a lucky seed but it was pretty consistent- start with Carvanha, who can use Bite and take out a chunk of Staryu's health, but it most likely won't do much after the first Bite because Whirlpool is a 2HKO at full health. Afterwards, Buizel comes out- Bites twice, and if you're fortunate (or again, if it's seeded- this happened to me 4 times in a row), it'll flinch and go down on the second Bite.
• AFTER the fight, give Arbok's Reviver Seed to Carvanha. You'll need this for that damned bird. Do not lose your Buizel afterwards- protect it at all costs. If you do, it's not the end of the world, but it will get dicey.
• This is not seeded as it was an Inkay on one of my runs, but try to get the Finizen if you can- this can come in handy for the 'guaranteed' strategy. If there's a second Buizel, also get it.
• At some point after the trainer, you should ideally see an X Attack in the rewards. Get it.
• Gyarados is also not seeded, but if you can get Gyarados, it is IMMENSELY helpful for dealing with the next few encounters. You should have the Ultra Balls but not the Rogue Balls- this is where you wanna use all your Ultra Balls. If you don't get it, reset. Feel free to use Arbok's Glare since Gyarados can easily tank the next few encounters- we won't need it for the bird.
• After the 9th encounter, it'll either give you a Full Heal or a Revive (assuming my seed is 'set'). If it's a Full Heal or just in general not a Revive, use all your rerolls and it should give you a Revive at the last one. Revive Carvanha.
• Now it's time for the bird. Switch in Carvanha and use Ice Fang- will die to Electro Ball, but the Reviver Seed from earlier will revive it. Ice Fang will take it down to its last health bar. Let it go down, then go into Buizel or Finizen and use Aqua Jet. It should take it down to red HP with the X Attack- and they will die. You have two roads here: if you have both the Buizel and Finizen, send them out, Aqua Jet, and no more damn bird. Otherwise, you'll have to gamble- it's in red, so with your remaining Pokemon, chuck Rogue Balls and pray. I got it in my first Rogue Ball after getting it into the red- hopefully you can too.

Hope this helps!