Square Enix has released screenshots of the new content in Chrono Trigger DS, including the two dungeons. Above is a screen of the most bizarre of the additions, the monster arena. In this mode you can control 50 different types of monsters and power them up to battle others. There's not too much that can be gleaned from a picture of two monsters facing off -- for example, whether combat is controlled by the player or determined entirely by the stats of each monster.
The dungeons include Dimensional Distortion, which spans across three time periods in one trippy dungeon, and the Dragon Sanctuary, which we hope wasn't a gimmick name. This dungeon takes place in the past and involves taking on quests to help the Reptites.