Flummoxed

Easy, fast and safe:

1. [npc=71163] (2,2,1)
2. [npc=86447] (1,1,1)
or.
2. Any Zandalari with Black Claw and Hunting Party

-Curse of Doom > Haunt
-switch to Ikky/Zandalari
-Black Claw > Flock/Hunting Party

Two pet strategy (not sure where to insert carry though):

Fel Pup (2, 1, 1)
Lost Netherpup (2, 2, 2)

Sequence:
1. Crouch.
2. Diseased Bite.
3. Howl.
4. Diseased Bite.
5. Diseased Bite.
6. Fel Pup dies; Lost Netherpup joins.
7. Shadow Shock.
8. Shadow Shock.
9. Howl.
10. Shadow Shock; Flummox dies.

Basically, you use Howl every time you are weakened, so your damage is maximized, and rely on the Beast racial to finish him at the tail end.

Flummoxed is randomly available in Suramar (25.20, 62.49) and only visible if you've unlocked World Quests.
Rewards will vary.

Master Tamer Flummox is a level 25 legendary with the following attacks: [pet-ability=1557], [pet-ability=1556], [pet-ability=111], passive buff: [pet-ability=956]

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• Tamer has two NPC pages (don't know why) where people are listing strategies in addition to the quest page. Quest, NPC1, NPC2.
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• Link to World Quest team/strat: here.
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• Originally at launch this tamer wasn't giving credit for Family Familiar - this has since been resolved.
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Master Tamer Flummox is part of Family Familiar
(Use the Spoiler tags to view the strats as they're developed/linked.)

Aquatic: Aquatic Acquiescence

• Team: [npc=71159] (2,2,2) | [npc=73359] (1,1,1) | [npc=70098] (1,1,1)
  Strategy: here | Credit: Purged

Gahz'rooki can be subbed with a (1,2,2) [npc=71017], but [npc=73359] & [npc=70098] have no alternates at this time.

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Beast: Best of the Beasts

• There seem to be a lot of variations for this fight with different combinations of spiders and pups:
  - If you have [npc=99527] (alts), [npc=93142], [npc=99526] (alts), use Randi's strategy (here).
  - If you have [npc=62864] (alts), [npc=72464], B/B [npc=62435] (alts), use Djongov's strategy (here).
  - If you have [npc=91823], [npc=93142], another beast, use TheManCalledZee's strategy (here).
  

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Critter: Mousing Around

• Option 1: [npc=64238] (1,2,2) (alts) + 2 critters with [pet-ability=165]
  Strategy: here | Credit: Chidsuey

This can be broadened to "a critter with [pet-ability=519]" and two "critters w/avoidance" - if not [pet-ability=165], then the [pet-ability=312]+[pet-ability=159] from a hare/rabbit/cottontail/bunny (list).

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Dragonkin: Dragons!

• Team: [npc=72463] (x,2,2) | [npc=9662] (2,2,x) (alt) | [npc=68662] (1,1,2)
  Strategy: here | Credit: kainwhisper

If you need help getting Yu'la from the Celestial Tournament, I had a lot of luck using mel9525's guide (here). Keep in mind you only need 12/15 tamers for the achievement, though.

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Elemental: Ragnaros, Watch and Learn

• Team: [npc=79039] (x,x,1) | [npc=73357] (2,x,2) | [npc=61703] (1,1,2) (only H/S and P/B are faster than Flummox, not sure if this matters)
  Strategy: here | Credit: Thatingles

Trying to find a middle pet to sub into ingles's strat that is more common, but so far no luck.

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Flying: Flock Together

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• Option 1: [npc=86716] (2,1,1) (alts) | [npc=86447] (1,1,1) | [npc=88452] (2,1,2) (alts-ish)
  Strategy: here | Credit: Lessiel
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• Two different versions with falcosaurs (orphaned hatchlings):
  - 3 falcosaurs with [pet-ability=518] & [pet-ability=1773] --- Strategy: here | Credit: Solacia
  - Snowfeather and Sharptalon Hatchlings (1,1,1 on both) + an owl with [pet-ability=184]+[pet-ability=256]+[pet-ability=517] (ex. [npc=97126]) --- Strategy: here | Credit: Xelians
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Humanoid: Murlocs, Harpies, and Wolvar, Oh My!

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• Team: [npc=90206] (1,1,1) | [npc=71014] (1,2,1) | 3rd Humanoid w/bigger attack, ex. [pet-ability=586]
  Strategy: here | Credit: Keepertje8

Looks like the breed of the Wolf can impact viability. See if the alternate moveset by briare (here) helps if you're having trouble.

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Magic: Master of Magic

• Team: [npc=71021] (1,1,1) | [npc=68658] (2,2,2) | [npc=71016] (?,2,?) (alternately: [npc=62317] (?,?,2))
  Strategy: here | Credit: Janathema

Strat is pretty straightforward, but commenters on OP have provided additional alts (like subbing [npc=68806] for Voidcaller).

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Mechanical: Roboteer

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• Option 1: [npc=68841] (2,1,1) | [npc=48609] (x,2,1) | [npc=88134] (1,1,1)
  Strategy: here | Credit: Avasam
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• Option 2: [npc=69778] (2,1,1) | [npc=73011] (2,1,1) | [npc=68841] (2,2,1)
  Strategy: here | Credit: Fedtmule
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Undead: The Lil' Necromancer

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• Option 1: [npc=71163] (1,2,2) | [npc=34770] (2,1,1) | 3rd Undead
  Strategy: here | Credit: Fedtmule
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• Option 2: [pet-ability=321] | [pet-ability=212] + [pet-ability=218] (list*) | Swarm ability ([pet-ability=1093] or [pet-ability=163] (list))
  Strategy: here | Credit: Ansawa
  *Ignore Unborn Valk on this list, spells share a slot.
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