Ride the Bantha, Dewback, Tauntaun, and the 4-legged Spider thing in Jabba's Palace. *MAYBE they want you to drive a few of the vehicles too, but I didn't ride the speederbike yet when I unlocked this. I've marked the vehicle locations with an asterisk.
If you play through the game's episodes and chapters in sequence you'll get this Achievement in the first part of Return of the Jedi.
Episode IV-2: Bantha, Dewback, Landspeeder*
Episode V-2: Tauntaun
Episode VI-1: 4-Legged Spider Thing
*Naboo Speeder: Episode I-5
*AT-XT: Episode III-4
*Landspeeder: Episode IV-2,3
*AT-ST: Episode IV-3