This may be the harshest challenge that Azumarill has faced yet, but water still beats ground in the end. Long story short, Venusaur's +2 Sludge Bomb can just OHKO Azumarill on Turn 1, and it feels like a coin flip whether you get Amnesia or not as the decider of if an attempt succeeds which takes a while when you need to wait for 85% timer to make the first move, and everything afterwards can still fall apart to an unlucky critical or poison proc. Even with locking in Gardevoir and Sylveon for healing and SpA drops, this was a very precarious battle, because Sylveon's AI decides not to Moonblast after Venusaur builds up its SpD so you don't actually get as much out of it as you would expect.
I picked out Sap Sipper and tera water for this fight specifically, with the usual Shell Bell and curated moveset of Amnesia/Liquidation/Mud-Slap/Belly Drum for special attackers. Unfortunately Petal Blizzard reveals Sap Sipper T0 so Venusaur doesn't get baited into choosing Giga Drain, but it still helps to be untouched.
My gameplan was to wait for the 85% time buff reset before my first move of Amnesia, and hope that Venusaur hits Amnesia to let me set up instead of Sludge Bomb to instantly kill me. Afterwards I have a bit more wiggle room with the defense cheer and set another Amnesia, then I set one Mud-Slap and try to Amnesia again while the defense cheer is still up. This Mud-Slap is helpful because otherwise if I set 3 Amnesias then I get stuck in a loop of having to rely on heal cheers and Life Dew to get back to full HP while Venusaur is always landing Sludge Bombs that ~3HKO my HP invested Azumarill, so Mud-Slap makes this a lot more possible with the chance of misses eliminating that damage. Sylveon landing a Moonblast can help but it has to happen early on before Venusaur gets fully set up as mentioned or the AI will prefer Quick Attack.
Afterwards I try to land 3 Mud-Slaps and then go tera Water with another Mud-Slap to remove my Fairy type and stop being weak to Sludge Bomb. Then I'm able to use heal cheers and hopefully get Belly Drum off safely. After that, I can start doing damage with Liquidations, which heal about ~100 from shield hits. In this attempt I basically just spammed Liquidation all the way home, trading crits (barely living Sludge Bomb thanks to Sylveon dropping SpA) before the shield break and getting some opportune defense drops + Leer support to keep the damage up in sun. In a past attempt I had lost out to Venusaur's double actions draining the timer and considered setting a Mud-Slap to skip some animations, but this time I just went all the way with Liquidation knowing I had those defense drops on my side.
Overall I would say this was definitely one of the riskier and more random raid clears of all time, relying on how the AI on both sides behaved to give me the chance to live. I was considering using cheer death preservation but wasn't sure if I could get a free turn on Venusaur after respawning. Maybe if I spammed Mud-Slap repeatedly I could abuse the chance of misses or something, but I'm not sure if time would allow for it. If anything, it was a uniquely frustrating experience to have to wait and see if I die turn 1 or not, so thank you game freak. I hope Blastoise is more forgiving.
As a sidenote, I keep noticing that whenever the boss hits me to exactly 300 HP or I heal to 300 HP, the HP numbers roll in more slowly. I have a few clips of this happening.