How do you lvl up fast in kingdom hearts 1?

The best way for me was by doing the tournaments in Olympus Coliseum because it's so long.

Very Low Levels: Phil Cup

Low Levels: Pegasus Cup

Medium Levels: Hercules Cup

High Levels: Hades Cup

If you haven't unlocked the Hades Cup, use the Phil Cup for low levels, the Pegasus Cup for medium levels, and the Hercules Cup for high levels.

And also if you don't feel like leveling up at the Olympus Coliseum, level up in a world you really like.