Chrono Trigger/Dimensional Vortex

In the Nintendo DS/Steam version, one exclusive area exists called the Dimensional Vortex. The Dimensional Vortex is a dungeon that can only be accessed after beating the game at least once. When you return to your saved game, three new Gates will have appeared in separate time periods (12,000 B.C., 1000 A.D., and 2300 A.D.).

Like other dungeons in the game, the Dimensional Vortex varies depending on which time period you're in when you pass through the gate. Each time period specifies the reward from completing the dungeon: a permanent upgrade to one of three characters.
 * Marle (the past)
 * Crono (the present)
 * Lucca (the future)

After completing all three different versions of the dungeon, a final, new, boss encounter is unlocked (as well as a new ending).

Dungeon entrance
Passing through any of the three Gates will take you to this area. You'll have to fight (or sneak) your way through several random maps from the game's locations before moving on.

After completing this first part of the dungeon, you'll enter into a room with a save point. Two additional paths lie in the room, one that takes you out of the Dimensional Vortex, and one that leads to the Twilight Grotto. This final area depends on which gate you entered through, and will also determine which boss you fight and which character receives a permanent stat boost.

12,000 B.C. dungeon
A large icy mountain that plays the unreleased song Singing Mountain. The special enemy is a Heckran like Snowbeast. At the end, you'll get to the Twilight Grotto where you'll fight a special boss if you haven't already done so. You'll move on to the "Twilit pool" and Marle will say something is calling her in. Move on to fight Alabaster Shade, a Marle look-a-like.

1000 A.D. dungeon
A large volcano dungeon. This dungeon is a recreated unreleased dungeon that has not appeared. The special enemy is Red Ghul.

At the end, you'll fight Once-King Dalton:

Dalton will be pretty angry that you beat him again, so he'll say something about going to Porre to raise an army. Although he says this, he will not appear anywhere in the town in either timezone. This is a reference to Chrono Cross in which Porre takes over the land where the game takes place and serves to set up a reasoning for Porre to invade.

At the Twilit pool, you'll need to have rescued Crono for the Steel Shade.

2300 A.D. dungeon
Another dome place. As usual there is relentless security. Do not miss out on finding the Apocalypse Arm treasure chest, Robo's broken weapon in the game that will deal 9999 damage on critical hit (equip the Dragon's Tear to make that more common). The special enemy here is the extremely powerful Iron Maiden. If you make it to the Twilit pool, you'll get to fight Lucca's shade, the Crimson Shade, and an additional foe, Eggsterminator.

Time's Eclipse
At the End of Time, speak to Gaspar and it turns out there have been goings on while you've been away. Enter the bucket to Time's Eclipse. Run ahead and meet up with Magus in his Prophet outfit. He'll speak of a new enemy who can devour dreams. He'll ask you not to interfere. He'll run into the gate leaving you with the choice to fight or not. Enter the gate if you think you are ready.

Beyond Time's Eclipse
Exit the gate to find a Lavos-like creature with Schala floating above it. Lavos will push Magus back into oblivion, and the fight will commence.

The Dream Devourer will be ready to take down existence when Future Magus manages to wake up Schala, who warps your party back to its own time. Schala will give a speech about how she's changed and sends Future Magus back to whence he came. Magus will wake up, and decide to recover from his amnesia. Congrats on getting the new ending. Once the credits are over, you'll see a new cutscene and obtain the DreamSeeker, Crono's most powerful weapon with 90% critical hit rate!