There are two new dungeons in Chrono Trigger DS: The Dimensional Vortex and The Lost Sanctum. One is a time warp that changes each time the player goes inside. The second is a new quest hub with a variety of tasks to complete.

The Dimensional Vortex is a new dungeon created for the Nintendo DS port of Chrono Trigger. It appears in three different locations in the game world and changes form each time the player ventures inside. Once entered, the player cannot leave before reaching the end. Overcoming the challenges within will result in changes at the End of Time.Official Site: Chrono Trigger Gameplay

The Dimensional Vortex can be accessed by defeating Lavos and beginning a New Game Plus. By defeating the bosses in each of the three locations, the player gains access to the game's new final boss and unlock the corresponding ending, "Dream's Epilogue."GameFAQs: Chrono Trigger New Dungeon Topic Search GamesRadar: Chrono Trigger Game Endings

The Lost Sanctum is a new quest hub that becomes available to players near the end of the game. The gate to the Lost Sanctum appears in both Prehistory and the Middle Ages. Players will encounter a people within the gate who offer increasingly more difficult tasks, which require the player to travel to different eras.Official Site: Chrono Trigger Gameplay

The Lost Sanctum becomes accessible after upgrading Epoch when the Black Omen surfaces. The rewards obtained in this dungeon are some of the best available in the game.GameFAQs: Chrono Trigger New Dungeon Topic Search