Square Enix's official blog for the Chrono Trigger DS port reveals some of the neat extras including Arena Mode.
The first installment dons the neat new arena mode where players can capture beasts found in the main game, train them up and do battle with other owners. To raise stats, monsters must be sent into the different time eras the main game spans - from prehistory to the future - where conditions and abilities used would be very different.
Acquiring a monster is easy, and it doesn't cost a thing. Once in the Arena talk to the Stable Master. He will give you a starting monster known as a smidge with your choice of one of the following elemental affinities: fire, water, light or shadow.
Be sure to keep your eyes on the Chrono blog for more updates.