Bodhi Sunwayver

He has only weak/dot-like abilities, just use Anubisath -> He kills all three allone.

For Aquatic Acquiescence I used

Pengu (1, 1, 1) (Alt: Tundra Penguin)
Moonshell Crab (1, 1, 1)
Any Aquatic pet

Spoiler

Itchy:

1. 
   
2. Peck until Itchy dies
3. 
   

Salty Bird:

1. 
   
2. Attack with anything until Pengu dies.
3. 
   

Switch out Moonshell Crab

1. 
   
2. Shell Shield>Renewing Mists
3. 
   
4. Arcane slash
5. 
   
6. Repeat
7. 
   

Grommet:

1. 
   
2. Shell Shield>Renewing Mists
3. 
   
4. Arcane slash
5. 
   
6. Repeat
7. 
   

Didn't use the third pet, so he can clean up if you mess up.

________________________________________________________________________________________

For Best of the Beasts I used

Death Adder Hatchling (1, 1, 2) (speed 276)
Feline Familiar (1, 1, 2)
Fel Pup (2, 2, 1) (May be avoidable)

Spoiler

Itchy:

1. 
   
2. Poison Fang
3. 
   
4. Puncture Wound
5. 
   
6. Blinding Poison(to dodge Whirlpool)
7. 
   
8. Poison Fang
9. 
   
10. Poison Fang
11. 
    
12. Poison Fang
13. 
    
14. Puncture Wound
15. 
    
16. Itchy should die.
17. 
    

Salty Bird:

1. 
   
2. Maybe a hit or two with Adder until it dies
3. 
   

Switch out to Feline Familiar

1. 
   
2. Stoneskin
3. 
   
4. Prowl
5. 
   
6. Onyx bite (should ruin the bird hardcore)
7. 
   
8. Salty bird should die.
9. 
   

Grommet:

1. 
   
2. Onyx Bite until Grommet dies.
3. 
   

If something goes horribly wrong, Fel Pup can clean up with Howl>Diseased Bite

________________________________________________________________________________________

For Mousing Around I used

Egbert (2, 1, 1)
Baneling (1, 2, 1)
Nibbles (2, 1, 2)

Spoiler

Itchy:

1. 
   
2. Keep Shell Shield up
3. 
   
4. Peck until Itchy dies
5. 
   

Salty Bird:

1. 
   
2. Peck until Egbert dies
3. 
   

Switch out to Baneling

1. 
   
2. Adrenal Glands
3. 
   
4. Baneling Burst
5. 
   
6. Should either kill or nearly kill Salty Bird
7. 
   

Switch out to Nibbles

If Salty Bird is alive:

1. 
   
2. Drain Power
3. 
   
4. Bone Bite
5. 
   

Grommet:

1. 
   
2. Howl
3. 
   
4. Bone Bite
5. 
   
6. Bone Bite
7. 
   

________________________________________________________________________________________

For Dragons! I used

Nether Faerie Dragon (1, 1, 2)
Emerald Proto-Whelp (2, 2, 2)
Chrominius (1, 1, 2) (May not be needed)

Spoiler

Itchy:

1. 
   
2. Cyclone
3. 
   
4. Slicing Wind
5. 
   
6. Evanescence
7. 
   
8. Keep up Cyclone and Slicing Wind until Itchy is dead
9. 
   

Salty Bird:

1. 
   
2. Keep up Cyclone
3. 
   
4. Use Slicing Wind until Nether Faerie Dragon is dead
5. 
   

Switch out to Emerald Proto-Whelp

1. 
   
2. Keep Emerald Presence up
3. 
   
4. Use Emerald Bite until Salty Bird is dead
5. 
   
6. Use Emerald Dream when below 50%
7. 
   

Grommet:

1. 
   
2. Keep Emerald Presence up
3. 
   
4. Use Emerald Bite until Grommet is dead
5. 
   
6. Use Emerald Dream when below 50%
7. 
   

Use Chrominius' Howl>Surge of Power if Proto-Whelp dies.

________________________________________________________________________________________

For Ragnaros, Watch and Learn I used

Pandaren Air Spirit (1, 1, 1)
Kirin Tor Familiar (2, 1, 2,)
Ruby Droplet (2, 2, 1)

Spoiler

Itchy:

1. 
   
2. Cyclone
3. 
   
4. Slicing Wind until Itchy is dead
5. 
   
6. If Pandaren Air Spirit dies, test your luck.
7. 
   

Sandy Bird:

1. 
   
2. Slicing Wind until Pandaren Air Spirit dies
3. 
   

Switch out to Kirin Tor Familiar

1. 
   
2. Spam Arcane Blast until Salty Bird dies
3. 
   

Grommet:

1. 
   
2. Spam Arcane Blast until Kirin Tor Familiar dies
3. 
   

Switch out to Ruby Droplet

1. 
   
2. Bubble
3. 
   
4. Plauged Blood
5. 
   
6. Aborb until Grommet dies
7. 
   

________________________________________________________________________________________

For Flock Together I used

Gilnean Raven (2, 2, 1) (But really just use your favorite flying pet)
Sentinel's Companion (2, 2, 1)
Glowing Sporebat (2, 1, 2)

Spoiler

Itchy:

1. 
   
2. (if your favorite pet, just keep hitting him. If Raven:)
3. 
   
4. Call Darkness
5. 
   
6. Nocturnal Strike
7. 
   
8. Alpha Strike until he dies
9. 
   

Salty Bird:

1. 
   
2. If Raven is alive, Alpha Strike until Raven dies.
3. 
   

Switch out to Sentinel's Companion

1. 
   
2. Moonfire
3. 
   
4. Soulrush
5. 
   
6. If still alive, Dark Talon
7. 
   

Grommet:

1. 
   
2. Dark Talon until Sentenel's Companion dies
3. 
   

Switch out to Glowing Sporebat

1. 
   
2. Creeping Fungus
3. 
   
4. Shadow Slash
5. 
   

________________________________________________________________________________________

For Murlocs, Harpies, and Wolvar, Oh My! I used,

You can solo with Anubisath Idol as mentioned by Terroklar2

But if that's too slow:

Lil' Bad Wolf (1, 1, 1)
Wretched Servant (2, 1, 2)
High level pet or clean up pet

Spoiler

Itchy:
Mangle
Howl
Claw
Claw
(use judgement of whether claw or howl is better here)
Howl
Claw

(if Lil' Bad Wolf dies, restart the battle)

Salty Bird:
Mangle
Claw unttil Lil' Bad Wolf dies

Switch out to Wretched Servant

Use Consume Magic to remove Cyclone
Nether Blast until Salty Bird dies

Grommet:
Use Consume Magic to remove Shattered Defenses
Use Consume to keep HP up
Nether Blast until Grommet dies

It was hard to incorporate a level pet for this fight. Maybe you can get one to have the last word.

________________________________________________________________________________________

Master of Magic, Roboteer, and lil' Necromancer on this comment (open in new tab if link doesn't work)

For the achievement Ragnaros, Watch and Learn I used the following pets:

Tiny Snowman (only one speed) with Magic Hat, Call Blizzard, Deep Freeze
Molten Corgi (only one speed) with Flamethrower, Superbark, Puppies of the Flame
Living Sandling (didn't use him at all so use any elemental pet here) with Punch, Stoneskin, Quicksand

Round 1: Tiny Snowman casts Call Blizzard
Round 2: Tiny Snowman casts Deep Freeze, stunning Itchy
Round 3: Tiny Snowman casts Magic Hat as Itchy swaps out for Salty Bird
Round 4: Tiny Snowman casts Magic Hat
Round 5: Tiny Snowman casts Magic Hat
Round 6: Tiny Snowman casts Magic Hat - Salty Bird should die here
Round 7: Tiny Snowman casts Deep Freeze as Itchy returns
Round 8: Tiny Snowman casts Blizzard as Salty Bird swaps out for Grommet
Round 9: Tiny Snowman casts Magic Hat
Round 10: Tiny Snowman casts Magic Hat and probably dies here, if not then cast another Magic Hat next round
Round 11: Molten Corgi casts Puppies of the Flame
Round 12: Puppies of the Flame continues
Round 13: Puppies of the Flame continues
Round 14: Molten Corgi casts Flamethrower, Grommet should die here - if not, another Flamethrower
Round 15: Molten Corgi casts Superbark on Itchy
Round 16: Molten Corgi casts Flamethrower, Itchy should die

Good luck!