There are 14 Trophies that can be collected.

BRONZE

Arcade complete!
[Arcade] Complete with any character (any difficulty)

Flame Distortion
[Arcade] Order Sol defeated.

Medal of Millionaire
[M.O.M] Completed.

Play through and you will not be let down
[Training] Trained for over 10 hours.

That's some skill you have
[Mission] Completed 5 mission with any character.

You are quite skillful
[Mission] Completed all missions with any character.

Our story has yet to come
[Story] Saw one ending.

Butterfly and Squall
[Ranked Match] First victory attained.

The goddess of defeat is finicky
[Player Match] First victory attained.

Accident core!
Even with a huge difference in health, you came from behind and won.

Hello World!
Game started.

SILVER

Slash Star
[Ranked Match] 100 battles fought.

King of Battles
[Player Match] 100 battles fought.

GOLD

Gold Order
[Survival] Attained lv. 999 and defeated Gold Order Sol.

http://www.ps3trophies.org/game/guilty-gear-xx-accent-core-plus/trophies/