Hidden Conditions
To trigger this PQ, you have to talk to Raditz in the Time Machine sector. He's near the entrance leading to the actual time machines. This will become available after finishing the first real Offline PQ. After completing the PQ the first time, it will be available in the PQ office for you to retry again.
You'll be fighting Goku and Piccolo in a 2v2 match. This battle has a steep difficulty curve for new players so if you're having problems enduring their attacks, grind on the other PQs to gain exp and zeni to boost your Attributes, get better equipment, buy items, or get new skills. Also, there's a chance that Gohan will appear if you defeat Piccolo first then finish Goku last.