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Well, this certainly is (dare I say it?) a titanic undertaking.

Some of my suggestions (those that I consider particularly on point in terms of the mythology, I've marked with *):

Land:

• Astrologer
• Aurochs
• Bowman
• Centaur*
• Champion*
• Chariot*
• Dagger
• Dayrider
• Grasshopper
• Helepolis*
• High Priestess*
• Left/Right Chariot*
• Lion
• Manticore (Rhinoceros)*
• Midnighter
• Moonrider
• Ram (Battering)
• Spider*
• Viper

Water:

• Nereid*
• Ship
• Turtle

Sky:

• East/North/South/West Winds
• Griffin*
• Hawk
• Hippogriff*
• Luna Pawn
• Owl*
• Phoenix*
• Sphinx*

And I hope I got all the links right. Most are from my Piece of the Day, and keeping the links straight is surprisingly difficult. (The rest of the links are from Piececlopedia.)

Anyway, that's what I could come up with offhand. I'll probably have more later.

PS: Feel free to peruse Unnecessarily Complicated Chess for anything that looks good. On my own perusal, I see (just going from top to bottom) Nightmare, Heroine, War Hawk, Swordsman, Oracle*, GemiKnight*, Unicorn, Harbinger, Dove, Pegasus*, Centauride*, Veteran, Shield Bearer, Medusa*, Torch, and Kraken*. You can probably find others.