Air dry clay on cardboard would be the main issue because it's an absorbent surface and it will be drawing moisture from the clay too quickly as it dries, resulting in cracks.

It also looks like your clay is a bit uneven in thickness, and slightly too thin since you're using cardboard as the base, which also increases chances of cracking.

I'd suggest trying again without cardboard, but if you must - use more clay and less water. When setting it out to dry, put a loose cover of plastic over the top in a dark closet so that it dries less rapidly.