I found the links between Chrono Trigger and Chrono Cross to be too shallow and unbelievable. I found the whole Schala-Kid connection to be meaningless and superficial at best. I'm sure I'm not saying anything particularly new here but the Chrono Trigger cast getting killed off screen was downright egregious. I never felt like I was playing a sequel to Chrono Trigger. It was more like playing a different game which had allusions to it.
That's super weird considering the ton of links, references and callbacks the game has. The El Nido archipelago is a set of artificial islands created by FATE, which is clearly stated to be an upgraded Mother Brain.
Then we have the presence of Belthasar, who is the actual mastermind behind the whole thing. We have the corrupted Masamune and even the presence of the actual spirits of the sword, Masa, Mune and their sister Doreen. The Zenan mainland gets mentioned constantly. The army colonizing El Nido is from Porre. A lot of the technology and magic objects in El Nido come from the Dragonians which are the evolved form of the Reptites. The Dead Sea you get to visit is actually the 2,300 a.D. future from Chrono Trigger being condensed/stored in that area and you find the corpse of Johnny, the racing robot, and also you get to see a computer report on the Day of Lavos, and at the end of it you witness the frozen, future state of the post-apocaliptic Leene's Square.
Guardia Kingdom is mentioned. And at one point in the game you even get to time travel back to the past to save Kid from Lucca's burning house. Then you get Lucca's super emotional letter to Kid.
The Dragon God itself was created as an organic nature control system by the Dragonians, which we made clear are the evolved form of the Reptites. Azala is even mentioned in the game.
Chronopolis was stated to be founded upon the ideas and research of both Belthasar and Lucca. One of the NPC's on Chronopolis mentions that he lives in Medina. Lavos is also being studied in Chronopolis, and the ancient Kingdom of Zeal is mentioned as a myth.
Chrono Cross has a lot more links, references and callbacks to its predecessor than many other sequels out there. If it wasn't for the time traveling shenanigans of the Trigger cast, not even the landmasses in Cross would exist, and since many of the characters that live in those islands are descendants of the researchers from Chronopolis, those character wouldn't even exist either.
To me, saying that the links between Cross and Trigger are "shallow" is like saying the links between the Metal Gear Solid franchise are shallow. The events of one game can only happen because of the events that happened in the other. Cross' plot cannot stand on it's own because it's a sequel, and it was always meant to be a sequel, and was written as such.