Here is the full list of all 46 JoJo's Bizarre Adventure: All-Star Battle trophies - there are 30 bronze, 13 silver, 2 gold and 1 platinum.
Collected every single trophy.
Cleared all of Story Mode.
Cleared Episode 2 in Story Mode Part 1.
Cleared Story Mode Part 1.
Cleared Episode 4 in Story Mode Part 2.
Cleared Story Mode Part 2.
Cleared Episode 3 in Story Mode Part 3.
Cleared Episode 6 in Story Mode Part 3.
Cleared Story Mode Part 3.
Cleared Episode 3 in Story Mode Part 4.
Cleared Episode 6 in Story Mode Part 4.
Cleared Story Mode Part 4.
Cleared Episode 1 in Story Mode Part 5.
Cleared Story Mode Part 5.
Cleared Episode 1 in Story Mode Part 6.
Cleared Story Mode Part 6.
Cleared Episode 2 in Story Mode Part 7.
Cleared Story Mode Part 7.
Cleared Story Mode Part 8.
Completed a match in Versus Mode with Player or COM characters.
Purchased 100 gallery items.
Purchased 500 gallery items.
Landed a HHA.
Landed a GHA.
Landed a HHA using Easy Beat.
Caused a Guard Crush to occur.
Pulled off a zoomed-in taunt.
Pulled off a Stylish Evade.
Pulled off a Flash Cancel.
Caused Rush Mode to activate.
Completed a Secret Mission for the first time.
Completed 30 Secret Missions.
Completed 50 Secret Missions.
Set off a battleground gimmick for the first time.
Set off all the battleground gimmicks.
You or an opponent were hit by a battleground gimmick for the first time.
Got hit by all the battleground gimmicks.
Pulled off a Dramatic Finish for the first time.
Pulled off all the Dramatic Finishes.
Finished a battle with a HHA or GHA.
Used Jotaro Kujo's "I stopped time..." style during DIO's "It's a steamroller!" GHA.
Landed Johnny's "Pretty long for a shortcut!" GHA on Valentine.
Landed Josuke 4's HHA supplementary move, "Meet my "homing missile!" on Kosaku Kawajiri.
Successfully performed Giorno's "Your "end" has no ending!" GHA.
Successfully performed Kars' "I am the ultimate life form" GHA.
Successfully performed Pucchi's "Maiden Heaven" GHA.