Distorted Time Eggs
Distorted Time Egg #1: Hercule's House - Complete all of the Great Saiyaman quests, then talk to Hercule.
Distorted Time Egg #2: Capsule Corporation - Complete the mission Sparring With Vegeta: Advanced, then talk to Bulma. Must be Lv50 to challenge.
Distorted Time Egg #3: Guru's House - Complete 15 successful defenses of Guru's House, then talk to Guru.
Distorted Time Egg #4: Buu's House - Feed Majin Buu enough food to create 6 family members, then talk to Majin Buu.
Distorted Time Egg #5: Frieza's Ship - Complete enough missions to turn Frieza into Golden Frieza or Cooler into Metal Cooler, then talk to the Frieza henchman with the green question mark.
Unlock Guru's House Bonuses
Additional Dragon Ball Wish Categories - Complete at least 15 defense missions, then talk to Guru.
Unlock Hidden Potential (Stat Cap Raise) - Complete at least 5 defense missions, then talk to Guru.