During the 2nd Timeron encounter (which is in the Space Battle stage) a timer will begin ticking from 00'00''00.
As the timer keeps going, the Timeron's attacks will change, and at every 20 minutes or so, a circular drone will appear, accompanied by Smash Daisaku's laughter. Avoid this drone for about 2 minutes until it self-destructs, for a single hit will reduce your health to zero.
At about 50'00''00 or so, large blue balls will appear. These will rebound once against the screen, and do 11 points of damage instead of the normal 10 points from the smaller ones.
Once the timer gets up to 99'50''00 or so, don't destroy the Timeron yet. Instead, wait out the remaining 10 seconds whilst avoiding the Timeron's attacks, but don't stay too close to the Timeron, or you'll get killed by the drone.
Once the timer reaches 00'00''00 again, you'll hear that nasty laughter again, but this time, ''GIVE UP!!'' appears in the middle of the screen, and the Timeron will self-destruct, accompanied by the message, ''YOU OPENED THE - SATORI MIND -''.
A bit more of that nasty laughter accompanies the next message, ''REPROGRAMMED BY NAMI - 1993''.
Now, instead of getting a Timer Bonus like you usually would, a Soul Bonus of exactly 930410 points is added to your score. That might be the date that Nami reprogrammed the Timeron, I believe.