Animals

Equestria, being a magical land, is populated by creatures that otherwise would be considered mythical. These rarely make more than one appearance, and typically represent obstacles for characters to overcome. Most reside in the Everfree Forest, well away from Ponyville.

Hydra
During the episode Feeling Pinkie Pie, a hydra was discovered to be living in Froggy Bottom Bog. It has four heads on long, snake-like necks, and a large, orange, dragon-like body without wings. Its behavior may have been territorial rather than predatory, as it gave up its pursuit once Fluttershy and the other ponies that disturbed it were out of immediate reach.

In classical mythology, there was only one hydra (meaning "water serpent"), the Lernaean Hydra, which was defeated by Heracles (Hercules) during his labors. It was so poisonous that even its breath and tracks were deadly, and if someone was lucky enough to cut off its head it grew two more.

Manticore
The manticore was encountered during Friendship is Magic, part 2 when Princess Luna enraged it to prevent Twilight Sparkle and her friends from finding the Elements of Harmony. It was calmed by Fluttershy's kindness.

In classical mythology, the manticore was a Persian creature with a red lion's body, a human-like face, a mouth with shark-like rows of sharp teeth, and a voice like a trumpet. Additional features such as a scorpion-like tail, wings, and the ability to launch poisonous spines at its enemies depend on the story, but have become standard in most modern representations. It has always been considered a man-eater, often leaving no remains, not even bones or clothing.