The party speaks to the Old Man about the new powers of the bucket, a transportation method at the End of Time in Chrono Trigger.

You’ve come a long way. You’ve travelled all of the ages, you’ve defeated Lavos at least once, you’ve probably watched one or two different endings, and you’ve seen all there is to see of the new content in Chrono Trigger... except, of course, for one battle. That's the Dream Devourer, the most powerful creature you can fight in Chrono Trigger.

To face the Dream Devourer you need to complete the three Dimensional Vortices that appear after you beat Chrono Trigger for the first time. Defeat the three Shades that appear at the end of each Vortex, then return to the End of Time. The Old Man informs the party that the bucket leading to the Day of Lavos has changed, and when you inspect it you'll find two destinations:
  • 1999, the Day of Lavos, which leads to the normal battle against Lavos
  • Time's Eclipse, which leads to the Dream Devourer
The Dream Devourer is a horribly powerful opponent, and the strongest you can face in Chrono Trigger. It also serves as a bridge between this game and its sequel, Chrono Cross. If you wanted an answer to a certain missing someone, you'll want to go to war against the Time Devourer. Get to level 60 at a minimum, then take the plunge.

The party battles the Dream Devourer, the greatest foe they can face in Chrono Trigger.

Dream Devourer

HP: 32,000
Absorbs: All elements (second phase only)

You thought Lavos was tough before? Wait 'til you get a load of its evolution, the Dream Devourer. Infused with the powers of Schala, the Dream Devourer uses the following attacks:
  • A Shadow attack that hits the whole party (first move)
  • Life Reaver, a chomping attack that steals HP from a single target
  • Pandemonium, a ground-shaking attack against the whole party
  • Supernova, a Light spell against the whole party
  • Incinerate, a Fire spell against the whole party
  • Ice Lance, a Water spell against the whole party
  • Gravity Sphere, a Dark spell against the whole party
  • Starfall, a non-elemental attack against a single target
  • Dreambind, which can inflict Stop on a single target
  • Mana Reaver, a counterattack spell that steals all of a single target's MP
  • Chaos Zone, a counterattack that can inflict Confuse on one or more targets
  • Phantasm, a strong magical attack against the whole party
  • The End of All and Nothing, a strong physical attack against the whole party
Unlike plain ‘ol Lavos, the Dream Devourer only has one form, and it looks quite familiar. The Dream Devourer is nevertheless very different from the Lavos you know and love, with greater attack power and some nasty tricks up its capacious sleeves.

The Dream Devourer starts off with a high resistance to... well, everything. It primarily attacks via elemental spells, most of them affecting your entire team. You’ll want one character healing constantly during this phase of the fight while the other two smash the Dream Devourer with their strongest magical attacks. You can use physical if you want, but the Devourer ofter counters with Mana Reaver, immediately draining the attacker’s MP. This applies to Dual and Triple Techs as readily as it does to normal attacks. Your magic won’t do a ton of damage, but it’s the best you’ve got.

Eventually the Dream Devourer ‘removes its defense’, greatly lowering its resistance to physical attacks. This second phase is deceptive, as it implies that you can go to town on the beast. You can, but not with elemental magic, as Dream Devourer absorbs any attack that’s not strictly neutral for the remainder of the battle. The Devourer counters every attack with Chaos Zone, so make sure your characters are protected against Confusion. The Dream Devourer also starts using even stronger magic attacks, and if anyone’s Confused they’ll do ridiculous amounts of damage. 

The battle against the Dream Devourer calls for four things:
  • Someone who's good with offensive magic (Crono, Marle, Lucca, Magus, arguably Robo)
  • Someone who can hit hard (Crono, Robo, Frog, Ayla)
  • Someone who can heal, even if it's just with items - and make sure you use all of your items, as battles don't get harder than this (all those Megalixirs you've been storing up, in other words)
  • Status-protecting equipment on all of your party members, to deal with Chaos Zone
For the first half of the battle you'll want your spellcasters to take the front lines and whittle away the Dream Devourer's HP. Once the beast's defenses come down, switch to physical attacks and let your casters take over healing. Crono is an excellent choice for your party since he bridges both areas of expertise, and can remain on the offensive for the entire battle, though you can get through this fight with any group you like - just make sure you keep their HP above 600 or so. The Dream Devourer can hit very hard.

Looking for a fun way to win this fight? As Chronopedia points out, the Dream Devourer has so much HP that it’s possible to overflow its health. Use Dual Techs with strong elemental leanings (I found combining Ayla and Lucca to be particularly effective in this) and you can make the Dream Devourer so healthy that you’ll win the fight. This method, though perhaps less satisfying, is probably easier overall, as the Devourer won’t counter with Chaos Zone when it’s healed.

Magus finds Schala, his sister, trapped within the Dream Devourer, a secret superboss in Chrono Trigger.

Beating the Dream Devourer earns you a new ending with strong ties to Chrono Cross. If you're playing the PC version this earns you the Dream's Epilogue Achievement. Regardless of version you’ll also receive the Dreamseeker, a sword for Crono that manages to outdo the Rainbow in damage output. By this point you've seen everything Chrono Trigger has to offer besides New Game + and other endings, so the Dreamseeker primarily exists to expedite replays. Enjoy!