You can only take part in this mini-game with Vivi at the beginning of Disc 3. Hippaul stands with his mother on the main street in Alexandria. When you speak to Hippaul's mother, Vivi and Hippaul will run a race.

Tap the Circle and Square buttons to run to the finish line. Hippaul's level increases the more you race him. For every 10 levels Hippaul gains, his mother gives you a card. You win new cards through level 70, plus a Key Item at level 80. You can actually level Hippaul up to level 100 (but you receive nothing for it).