Sega Vintage Collection: Golden Axe

There are only 3 type of creatues to ride in the 1st Golden Axe. 1st level has the cockatrice that attacks by whipping it's tail. 2nd level has a dark colored dragon that breathes fire onto the ground. At the start of the 3rd level is a red dragon that shoots fireballs. Ride one of each of those 3 types and you'll get your achievement.

First stage there's many of the dragons you can ride that swings tail & spit fire.I got this achievement on the stage right after that where there's a red dragon that shoots fireballs.