Here is a video guide to help you find all the monsters you can ride on.
Please keep in mind that the last monster cannot be found until you re-visit Gallopolis during Act 2. Good luck!
Also, I’ve provided the locations in word form for you if you want results faster.
Eggsoskeleton - Kingsbarrow
Skull Rider's Steed - Cryptic Crypt
Horknight's Hornet - Laguna di Gondolia
Face Invader - Snaerfelt
Dragon Rider's Dragon - Mount Pang Lai
Headless Horseman's Horse - Gallopolis Desert (Act 2 onwards only)