Dragon Ball Z Budokai HD Collection

(DU = Dragon Universe)
Cooler: The most important note in unlocking Cooler is to complete Vegeta's DU, as well as
Goku's DU. Play through Goku's DU a second time. After your battle with
Frieza, there will be three red dots on your map of Namek. Proceed to the red
dot directly below where you faced Frieza, and you will have to battle Super
Saiyan Vegeta. Once you defeat Vegeta, head towards the red dot near the
middle of the screen. This dot will initiate Cooler's appearance, and upon
defeating him, Cooler will be unlocked.

Note: While Cooler can be battled in various ways with various characters in DU
mode, he can only be unlocked through the process listed above.

Bardock: As soon as you begin Goku's DU a second time, search the northern
mountains for Raditz' Spaceship/pod. When you find it, enter it, and you
will receive Bardock

Broly: In order to unlock Broly, you must play through Goku's DU Story a second time after having
completed it once before. The next step is to reach the Majin Saga,
specifically the point where Goku is looking for someone to fuse with via the
Potara earrings. This segment occurs right after the scene where Gohan is
absorbed by Super Buu. First, look in the immediate area surrounding where
Goku starts this stage. A ??? nearby should start a conversation with Hercule.
Once that scene ends, head towards the red dot on your map, but do not begin
the battle with Super Buu yet. Near the battle with Buu, will be another ???
mark what will show a scene with Tien. Once that is finished, search the
surrounding area for a location that reads 'Mountains'.

If you have found the correct location, a dialogue with kabitoshin will ensue,
where he discusses a greater evil being on the earth, and how he is intimidated
by the fact. Once this dialogue has ended, feel free to fight Super Buu. Once
you defeat Super Buu within Buu's body, there will be a new dialogue where
Vegeta will hold off Buu so that Goku can investigate the new force. A new red
marker will appear on the map, where Broly will be waiting. Defeat him, and
Broly will be unlocked for all modes, including DU.

Note: Broly can be faught by Vegeta on a second play through of Vegeta's DU
mode. Head to the island covered in snow before fusing with Goku to battle
Super Buu, and you will have an automatic dialogue with Kabitoshin about Broly.
After the dialogue, battle Buu as normal, and you will eventually face Broly.
Using Vegeta will not unlock Brolly, but it is necessary to fight him for some
of Vegeta's rare capsules.

Note2: Broly can also be faught by Gohan (Adult) as happens in the actual movie
and in the Broly's DU mode, during a second playthrough of Gohan's (Adult) DU
mode, but this will not unlock Broly. .

Omega Shenron: To face off with Omega Shenron, you will need to be playing through Goku's DU
mode on a second time or more. In order to battle Omega Shenron, you need to
have collected Goku's SSJ4 Capsule. With this prerequisite set, fulfill the
requirements for fighting Broly as listed above. Once you have beaten Broly,
ignore the red dot on your map and proceed to West City where Goku will have a
dialogue with Bulma about the Dragon Radar. Proceed to the red dot on your map
now, and defeat Gotenks using the Gogeta fusion. Once you have done so, a new
red dot will light up on your map, where you will find Omega Shenron. SSJ4
Vegeta will arrive, and he will fuse with Goku to form SSJ4 Gogeta and you will
battle Omega Shenron in this form. Defeat Omega Shenron in an incredibly easy
battle, thanks to the power of SSJ4 Gogeta, and you will unlock Omega Shenron,
as well as Goku's SSJ4 Gogeta capsule.

Note: Some players claim that collecting the DragonBalls is not required for
this series of events.

Source: http://www.gamefaqs.com/ps2/920505-dragon-ball-z-budokai-3/f...
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My notes:
After you defeat Broly as Goku in Goku's DU, fly around the southeast part of the maps along the tiny islands by Master Roshi's house and there will be a ??? location, land here and you will obtain the SSJ4 Goku capsule. Equip it right away then go to west city and talk to Bulma and then the red dot will move to the World tournament. Do that and you will unlock Gogeta after the fight and as soon as the fight ends your next red dot will be to fight Omega Shenron. With your SSJ4 Goku capsule equipped, when you fight him you will be able to obtain SSJ4 Gogeta. So all in all, in one run you should be able to obtain Cooler, then Broly, SSJ4 Goku, Gogeta, SSJ4 Gogeta, then Omega Shenron all in that order. The only way you will obtain Cooler is if you have completed Vegeta's DU for the first time though. Have fun :)