Bardock and Future Gohan

Distorted Eggs are special items you can get from the rifts across Conton City, you must do the quest lines of each rift to get them, when you get all 5 you will have to deliver those to the Time Supreme Kai then you will trigger new events.

Buu´s House: Get all the 6 members of the family. Buu will give you the egg
Capsule Corp: Finish all Vegeta´s trainings, then get it from Bulma.
Freeza´s Spaceship: Finish the entire line until freeza gets Golden transformation, in this order, Zarbon or Dodoria side, Ginyu tasks, Freeza´s quests, then you will get the egg from a soldir right outside of freeza´s room.
Guru´s House: Finish the quest line, then you will get it from the Guru.
Hercule´s House: Finish the quest line from the Great Saiyaman, doesnt matter if you haven´t finished Hercule´s tasks.

When you deliver all distorted eggs to the Supreme Kai of time, she will trigger new events, i zoned to get the new time patrol quests, then go to Trunks and start the quest.

Such quest will be the fight between Bardock and Mira, is not an easy fight, good luck with that, then you will have a text choice:

It´s dead
Fighting somewhere else

i picked "fighting somewhere else", then you can get out to from the time nest and go to this location:

After that even without zoning you can start the other secret quest, Future Gohan´s fight, finish the fight then you will get to choose between:

Arrange mistake (or something like that)
Leave it be

i picked leave it be, apparently choices have nothing to do with the result, but i haven´t tested that, then zone from the time nest and go to the next location:

Enjoy your mentors.