To get this ending during the “New Game Plus” you must fight Lavos after crossing the Zenan Bridge for the first time in 600 AD. I believe this must be done before obtaining the hero medal from Tata. Once again Lavos can be fought by going through the bucket at the end of time or by going to the fairgrounds in 1000 AD. The advantage to the later is that you will not need to fight all of the attack modes of Lavos while he is still in shell form. You will just need to fight the final attack mode to destroy the head once.
Basically this ending consists of Tata deciding to go after Magus but Crono and company beat him to the task.