Frio and Kyaro, two teenagers, love the Tales legends and read about them every day before they go to sleep. After an earthquake, Dr. Brown finds an ancient time traveling machine in the ruins. Using this, they can go see the Tales legends. They go to sleep and prepare for tomorrow. Before Frio went to sleep, he read a Tales legend again. But this one ended strangely: the hero arrives too late and the world is destroyed.
When Frio and Kyaro wake up, they find out the machine has been stolen. Not long after they find out, a re-color of the machine appears. The one boarding it was Dr. White, Dr. Brown from 100 days into the future whose hair had turned white from extreme stress.
There are thieves who are ruining the timeline of the Tales legends, and they have to be stopped. Dr. White now needs Frio and Kyaro to help stop the thieves and brings with him the aid of the heroes from Tales of Symphonia, Destiny, and Eternia.
Source: Wikipedia, "http://en.wikipedia.org/wiki/Tales_of_the_World:_Narikiri_Dungeon_3," available under the CC-BY-SA License.