In Story Mode, beat Dabura with Teen Gohan.

Unlock Bardok

In the begging of DU, when you fly over the Raditz's spaceship, you will see a ???.  Enter it.

Unlock Brolly

The second time you play the game, beat Brolly as Goku (not Kid Buu).

Unlock Fat Buu

Play through the dragon universe with Goku.

Unlock Kid Goku

Beat Dragon Universe Mode with Broly.

Unlock Teen Gohan

Beat Dragon Universe Mode with Kid Gohan.

Unlock the Dragon Arena

Beat all the DUs (except for Brollie's).