Can You Get Legendary Creatures in Red Dead Redemption (Xbox 360)?

No. Legendary creatures were added exclusively in the Undead Nightmare DLC, which released on Xbox 360 and PS3—but only as part of that DLC.

If you only have the base Red Dead Redemption game on Xbox 360, you do not have access to Undead Nightmare or its legendary creatures (e.g., Chupacabra, Sasquatch, Four Horses of the Apocalypse).

Purchase Undead Nightmare separately (digital) or get the Game of the Year Edition which includes it.