Kyurem-Black is a strong contender for being the single best Pokemon in the game, competing only with Psystrike Mewtwo. It has a monstrous 310 Base Attack, 10 points higher than Mewtwo's, with higher bulk than Mewtwo. The most important thing about Kyurem-Black: it received Dragon Tail/Outrage, which is the best Dragon-type moveset it could have hoped for.
All these factors combine to create a monster that does around 10% more DPS than the previous-best Dragon-type, Rayquaza, with around 30% more bulk. If you care at all about having strong Dragons, you will want to raid this as much as possible.
The trio is relatively easy; almost every Dragon-, Fighting-, Rock-, Fairy-, or Steel-type on this list, powered up to around Level 30, will be able to pull off the trio. Outrage is scary if you're using underleveled Dragons, but you can just use other types, or dodge Outrages.
The duo is much harder, but it is still achievable within reason (unlike, say, the unboosted Zekrom duo).
Minimum viable levels assume Best Friends, no Weather, no Dodging.
Italics indicate a Legacy move.
Level 40 Palkia and Dragonite are duo-viable against Shadow Claw/Iron Head, but are slightly too weak to consistently duo against Dragon Tail/Iron Head. If you have enough high-level Meteor Mash Metagross carrying, you can afford to slot in a few Palkia or Dragonite.
Metagross is king against all Kyurem movesets; the more Metagross you have, the more you can afford to slot in other, weaker Pokemon without jeopardizing your chances of winning.
Note that Metagross must have Meteor Mash; without Meteor Mash, Metagross is non-viable for the duo, even at Level 40.
Level 40 Machamp is slightly too weak to duo against Stone Edge by itself; if you have enough high-level Metagross to make up for the time difference, you can afford to slot in one or two Machamp.
If you can consistently dodge Stone Edges, Level 40 Dragonite, Rayquaza, and Outrage Salamence are duo-viable.
If you can dodge, Level 40 Rampardos and Dialga are duo-viable against Blizzard.
With dodging, Level 40 Rayquaza and Outrage Salamence are duo-viable against Dragon Tail/Blizzard, but fall slightly short of being duo-viable against Shadow Claw/Blizzard.
Level 40 Dialga is borderline duo-viable against Outrage without dodging; it's technically viable against Shadow Claw/Outrage, but falls slightly short of viability against Dragon Tail/Outrage.
Level 40 Palkia and Garchomp are duo-viable against Shadow Claw/Outrage with dodging, but not against Dragon Tail/Outrage.
Against Dragon Tail/Outrage, Level 40 Garchomp is borderline duo-viable with dodging; if you have high-level Metagross carrying, and you're confident in your ability to dodge Outrages for 5 straight minutes, Garchomp can be slotted in.