For boss information, see Heckran (Monsters).
The Heckran is a beast who apparently has control over a few Mystics in 1000 A.D. He lives in Heckran Cave, which provides passage to the sea near Lucca's house. His major function is to alert Crono that Magus summoned Lavos years ago. It's revealed in the Prerelease that Magus ordered Heckran to protect the spot over which Lavos sleeps.
The Heckran in Chrono Trigger appears to have an allegiance to the Mystics. However, in Radical Dreamers and Chrono Cross, the Heckran seems to be referenced as a mere wild beast. A Heckran Bone is a key item, and be used to attract Poshul.