List of pets that receive both damage and defense bonuses

[Felixinseattle]

]VS Aquatic

• Enchanted Broom — [Enchanted Broom]
  
  JadeOwl — [Jade Owl]

Vs Beast

• Brilliant Spore — [Brilliant Spore]
  
  Cerulean Moth
  
  Crimson Spore — [Crimson Spore]
  
  Crimsonwing Moth
  
  Dragon Kite — [Dragon Kite]
  
  Dusty Sporewing — [Dusty Sporewing]
  
  Mechanical Axebeak — [Mechanical Axebeak]
  
  Seaborne Spore — [Seaborne Spore]
  
  Skywisp Moth
  
  Stormwing — [Stormwing]
  
  Umbrafen Spore — [Umbrafen Spore]
  
  Zangar Spore — [Zangar Spore]

VS Critter

• Bonkers — [Bonkers]
  
  Corefire Imp — [Blazing Rune]
  
  Curious Wolvar Pup — [Curious Wolvar Pup]
  
  Dandelion Frolicker — [Dandelion Frolicker]
  
  Deathy — [Smoldering Murloc Egg]
  
  Fiendish Imp — [Satyr Charm]
  
  Flayer Youngling
  
  Grommloc — [Grommloc]
  
  Harbinger of Flame — [Mark of Flame]
  
  Hogs — [Hogs' Studded Collar]
  
  Kun-Lai Runt
  
  Lil' Bad Wolf — [Spiky Collar]
  
  Stunted Yeti

VS Dragonkin

• Bone Serpent — [Bone Serpent]
  
  Cursed Birman — [Cursed Birman]
  
  Fragment of Desire — [Fragment of Desire]
  
  Macabre Marionette — [Macabre Marionette]
  
  Scourged Whelpling
  
  Weebomination — [Weebomination]
  
  Widget the Departed — [Widget the Departed]

VS Elemental

• Rapana Whelk
  
  Rusty Snail
  
  Scooter the Snail — [Snail Shell]
  
  Shimmershell Snail
  
  Silkbead Snail

VS Flying

• Azure Whelpling — [Azure Whelpling]
  
  Bronze Whelpling — [Time-Locked Box]
  
  Celestial Dragon — [Celestial Dragon]
  
  Chrominius — [Whistle of Chromatic Bone]
  
  Emerald Proto-Whelp
  
  Emerald Whelpling — [Tiny Emerald Whelpling]
  
  Essence of Competition — [Competitor's Souvenir]
  
  Infinite Whelpling
  
  Lanticore Spawnling — [Lanticore Spawnling]
  
  Nether Faerie Dragon
  
  Netherwhelp — [Netherwhelp's Collar]
  
  Nexus Whelpling
  
  Spirit of Competition — [Gold Medallion]
  
  Sprite Darter Hatchling — [Sprite Darter Egg]
  
  Yu'la, Broodling of Yu'lon — [Yu'la, Broodling of Yu'lon]

VS Humanoid

• Amethyst Spiderling
  
  Ash Spiderling
  
  Crystal Spider
  
  Desert Spider
  
  Devouring Maggot
  
  Dusk Spiderling
  
  Fel Pup
  
  Festering Maggot
  
  Feverbite Hatchling
  
  Forest Spiderling
  
  Jumping Spider
  
  Jungle Grub
  
  Larva
  
  Lost Netherpup — [Lost Netherpup]
  
  Maggot
  
  Molten Hatchling
  
  Mr. Grubbs — [Mr. Grubbs]
  
  Skittering Cavern Crawler
  
  Smolderweb Hatchling — [Smolderweb Egg]
  
  Spider
  
  Twilight Spider
  
  Venomspitter Hatchling
  
  Widow Spiderling

VS Magic

• Mechanical Pandaren Dragonling — [Mechanical Pandaren Dragonling]

VS Undead

• Biletoad
  
  Darkmoon Turtle — [Darkmoon Turtle]
  
  Emerald Turtle
  
  Frog
  
  Garden Frog
  
  Gulp Froglet — [Gulp Froglet]
  
  Horny Toad
  
  Huge Toad
  
  Jubling — [A Jubling's Tiny Home]
  
  Jungle Darter
  
  Leopard Tree Frog
  
  Mac Frog
  
  Mojo — [Mojo]
  
  Mud Jumper
  
  Small Frog
  
  Softshell Snapling
  
  Speedy — [Turtle Box]
  
  Spiny Terrapin
  
  Spotted Bell Frog
  
  Swamp Croaker
  
  Toad
  
  Tree Frog — [Tree Frog Box]
  
  Turquoise Turtle
  
  Wood Frog — [Wood Frog Box]
  
  Yellow-Bellied Bullfrog

I didn't do VS mechanical since just about all elementals do elemental damage.

[Jerebear]

I tend to add Willy as an aquatic one as well. With the moveset Tongue Lash, Eyeblast, Rot, he does Strong damage to aquatics and takes weak damage from them as well. Not a perfect hard counter, but an interesting one based on moveset.