The special endings depend on when you defeat Lavos, not how.
  • Defeat Lavos before departing to A.D. 600.
  • Defeat Lavos after returning from A.D. 600 but before Chrono gets thrown into jail.
  • Defeat Lavos after emerging from the Vortex. You can also get this ending by beating Lavos in the Ocean Palace.
  • Defeat Lavos after defeating Zombor but before receiving the Hero's Medal from Tata.
  • Defeat Lavos after you get the Hero's Medal but before traveling back to 65,000,000 B.C.
  • Defeat Lavos after returning from 65,000,000 B.C. but before delivering the Grand Lion to Frog.
  • Defeat Lavos after giving Frog the Grand Lion but before fighting Magus.
  • Defeat Lavos after fighting Magus but before crushing the Reptites.
  • Defeat Lavos after defeating the Reptites but before Sara opens the seal.
  • Defeat Lavos after Sara opens the seal but before everything goes to hell.
And, of course, there are many permutations of the regular ending, depending upon whether you crashed the Epoch, whether you killed Magus, and whether you erased Chrono's death from history.