Rainbow Shell (Fragmentation of)
Why is there one Rainbow Shell in Chrono Trigger, yet many fragments in Chrono Cross?
After Porre conquered Guardia, they came into posession of the Rainbow Shell. Given the militaristic state of the world, it befell some accidental fate, possibly involving an explosion, that fragmented it into several pieces. Through the Acacia Dragoons, merchants, and Porre's vested interest in El Nido, these pieces made their way to the islands.
Legend of the Past
Since Dinopolis is from the Reptite Dimension, perhaps the Rainbow Shell from prehistory in that dimension came to be stored in the Dragonian metropolis. When Chronopolis bombed Dinopolis during the war in El Nido, that Rainbow Shell was fragmented into several pieces around El Nido.
From: Theory (Objects)