Azumarill and this Poison-weak/Fairy-heavy NPC squad soloed Hydreigon reasonably quickly in only a few attempts (after the given prep time of locking in some proper NPCs, and moving my EVs around from Def to HP). I was looking for Bellibolt for Light Screen + consistent Discharge support, but got all the other 3 opportune supports of Arboliva/Sylveon/Gardevoir for maximum healing and Moonblast for the only source of potential SpA drops to counter Nasty Plot (plus Charm post-shield-break).
(One attempt right before failed to a Tera Blast crit.)
Azumarill itself has the standard set of Shell Bell/Huge Power/tera Water STAB and Liquidation/Amnesia/Belly Drum setup, with Body Slam filling the last slot as a tera charger and potential paralysis in the stead of Mud-Slap thanks to Levitate. Muddy Water may have feasted well here but I don't use DLC TMs (or transfer-only options, basically just base game availability).
The gameplan here is pretty straightforward. Azumarill can use Liquidation or Body Slam T1 for tera charge and survive a Tera Blast while the NPC defense cheer goes through, then die on T2 while setting an offense cheer to perserve both stat cheers permanently as usual. Body Slam is technically riskier with the chance of early paralysis messing up the intentional faint, but I like to track my PP separately.
0+ SpA Tera Poison Hydreigon Tera Blast (80 BP) vs. 252 HP / 0 SpD Azumarill: 276-326 (68.3 - 80.6%) -- guaranteed 2HKO
After that, Azumarill just needs to gun it and set up to 3 Amnesias (if dead on T2, Hydreigon seems to get its Nasty Plot right before Amnesia 3), which is a lot easier to pull off with healing support and potential Moonblast drops. With no Life Dews, I have seen Azumarill die to a high roll +2 Tera Blast even at +4, but I would say this has a fair chance of success.
0+ SpA Tera Poison Hydreigon Tera Blast (80 BP) vs. 252 HP / 0 SpD Azumarill through Def Cheer: 186-218 (46 - 53.9%) -- 46.5% chance to 2HKO
From there, not much else to do but Body Slam and fish for paralysis, which can be triply helpful in terms of denying Hydreigon attacking turns on both Azumarill and any NPCs that could appreciate getting a heal off (and potentially Nasty Plot), as well as letting Azumarill and those NPCs outspeed to get more attacks/setup in (at least before Dragon Dance), and just needing one paralysis proc to stick for the rest of the fight thanks to there being no debuff resets afterwards. Fortunately I got the paralysis on my first Body Slam on this attempt, on top of some opportune heals.
From there I got Body Slam 2 off to get full tera charge, then sent the last two heal cheers back to back to try and set up safely for Belly Drum. Heal cheer 1 sent me from 149 to 310 HP (161 HP/40% heal), though I still went down to just above half HP from the incoming Tera Blast (232 HP), which was also right before the 55% time Nasty Plot that got denied by paralysis and might have saved me from not being able to Belly Drum here. Grassy Terrain tipped me up to 257 HP at the end of turn but I didn't get a Life Dew, which wouldn't be enough to drum and live another Tera Blast.
(Actually in hindsight, I could have terastallized and made it not super effective, facing this at 55 HP:
+2 0+ SpA Tera Poison Hydreigon Tera Blast (80 BP) vs. +6 252 HP / 0 SpD Tera Water Azumarill through Def Cheer: 46-55 (11.3 - 13.6%) -- possible 8HKO
So I guess it would have been fine to drum there and heal from Shell Bell afterwards, but it could have risked dying to max roll.)
Heal cheer 2 got me to full HP from 257 HP, with Tera Blast doing light damage after another Grassy Terrain heal. This is the point where I actually went for Tera Water Belly Drum.
Around this time, it seemed that Sylveon had procced one Moonblast drop as I was fully set up and ready to start the onslaught of outspeeding Liquidations. Hydreigon switched to some similarly neutral but ineffective Dragon Pulses, while two Liquidations was enough to barely just not break the shield (though the AI chipped it down anyway.)
+6 252+ Atk Huge Power Tera Water Azumarill Atk Cheer Liquidation vs. 0 HP / 0 Def Tera Poison Hydreigon: 1472-1732 (18.1 - 21.3% of 25x hp boss) -- possible 5HKO
+1 0+ SpA Tera Poison Hydreigon Dragon Pulse vs. +6 252 HP / 0 SpD Tera Water Azumarill through Def Cheer: 37-45 (9.1 - 11.1%) -- possible 9HKO
With the shield break came the HP% buff reset, so I took the free shieldbreak turn and the next outspeeding turn to set 2 Amnesias back up before Hydreigon could land another hit. After seeing the damage of a Dragon Pulse against +4 Azumarill do nothing while Life Dew brought me back to full, I decided to forgo a 3rd Amnesia and just go back for Belly Drum.
By now, Sylveon had landed another Moonblast proc as well as Charm to dissuade physical Tera Blast, while Azumarill was pretty much ready to end the fight.
2 more Liquidations was enough to end it, with a defense drop for good measure. Dragon Dance finally went through at 40% HP along with it going into the random double attack phase, but fortunately it wasn't able to capitalize on it for long.
Overall, another pretty solid showing for Azumarill with a harsh first half to prepare for, but the actual damage dealing aspect being smooth sailing. I suppose only a 25x HP multiplier on the lower end and very little stat resets makes up for the double Nasty Plot here, but I won't be complaining about good luck with the matchup being tough enough as is.