Instructions
Collect enough experience points from battles and quests to reach Level 10. Speak to Belle at the Secret Plaza of the Resistance Headquarters in Edelstein.
Accept the "Path of the Wild Hunter" quest to set your character class to Wild Hunter.
Speak to Belle again and accept the "Taming a Jaguar" quest.
Speak to Black Jack on the same map as Belle and he will transport you to the Jaguar Habitat map.
Approach the jaguar you want to use as your mount and attack it. Wear its health down to less than half, then use the Capture skill to catch it. You can now use the Jaguar Rider skill to ride your captured jaguar.
Capture another jaguar of a different color to use it as your mount instead. You only ever have one jaguar, so the color of your mount will correspond to the last jaguar you captured.