If you want to unlock stuff for this game then you'll be spending most of your time in the online-only Campaign Mode. So here's some hopefully helpful info for the people stuck behind the language barrier.
Before you do anything, make sure you go to the PSN Store (JPN or HK) and get the free DLC for this game which is a 100+MB download. Without that, you can't play the first campaign which is the only one currently available.
The first time you (successfully) log into the campaign menu, a full screen wall of text will appear. This is the T&C so scroll to the bottom to have "read" everything and press O to confirm. A second pop-up will appear now highlight the top option and press O again to confirm. You may need to adjust accordingly since I don't know if the game swaps O/X depending on your machine.
Every other time you go into the main Campaign screen, you'll see a pop-up window, this is just a list of updates and/or how well your avatar did for you while you were offline.
On the top right of the Campaign page is a battery icon with 10 bars. That is the amount of charge you have to do anything in this mode. 1 bar recharges every 20 minutes so when you've used them all up, it'll take a bit over 3 hours to fully recover.
Campaign has 4 options from top to bottom: Campaign; Medal List; Ranking; Support Items.
Medal List - A list of every medal you've collected for each character. Medals represent all the customisation items you have access to, poses, colours, dialogue lines, etc.
Ranking - View other people and your/their rank online.
Support Items - Goes to the PSN store and buy help for real world money.
Campaign Mode - Everything from here onwards will be related to the main mode.
Inside campaign mode, you will see a list of available campaigns (only one at the time of this post).
Select one and a pop-up will appear with a choice: Search for a boss (1 charge) or cancel back out.
When searching, you'll run across one of two types: Visions and Bosses. Visions are online avatars of other players. Bosses are AI bosses made for the campaign.
Beating Visions or Bosses will get you 1 medal each time. Beating a boss will also take a chunk off their main HP gauge. Reducing that gauge to 0 will net you a few medals.
Before fighting, you have 2 choices: pick a character and use a support item. When fighting a Boss, you can also press left or right to use up more charge to do more damage to their global HP in this encounter. I recommend not using it so you have more encounters/more chances of random help appearing.
Random Jojo characters will appear to give you some help during the campaign mode with various effects. Here's some examples:
Tonio Trussardi - Appears after fights and recovers 1 charge for you.
Cairo Informant - Appears during search and will offer to let you chose a specific boss for 2 charges.
F.F - Appears before a fight and offers you a choice of increased attack or 1 recharge.
Rudolph von Stroheim - Appears before a fight, reduces their HP.
"He who understands is not better than he who appreciates, he who appreciates is not better than he who enjoys." Confucius