To unlock the Bardock and Broly Saga, you need to find all five shards. You can do so by following the instructions below.

1 - Defeat Quest 3 in the Demigra Saga.
2 - Speak with Recon at Time Square.
3 - Complete Parallel Quest 49.
4 - Defeat Goku in Parallel Quest 14, or defeat Ginyu in Goku's body during Parallel Quest 18.
5 - Complete Parallel Quest 2, or defeat Super Saiyan Goku in Parallel Quest 21.

With all of the shards in your possession, talk to Trunks and you will begin the secret Saga mission.