There are 14 Trophies that can be collected.

Bronze

You're Cooked
Defeat Saki in Normal or Hard Arcade Mode before time runs out.

Pew Pew, Iru Iru
Defeat Iru in Normal or Hard Arcade Mode before time runs out.

Napolean Complex
Defeat Nanako in Normal or Hard Arcade Mode before time runs out.

Burning Up on Re-entry
Defeat Kae in Normal or Hard Arcade Mode before time runs out.

You'd Better Ice That
Defeat Kyoko in Normal or Hard Arcade Mode before time runs out.

There Can Only Be One
Defeat Suguri in Normal or Hard Arcade Mode before time runs out.

Dancing Days
Defeat Hime in Normal or Hard Arcade Mode before time runs out.

Float Like A Butterfly
Win a fight without taking damage in Arcade Mode.

Keep Your Cool
Win a fight without reaching 150% on the heat gauge in Arcade Mode.

Like A Drum
Land a 30 hits combo or higher in Arcade Mode.

Time's Up
Win 5 matches in Normal or Hard Arcade Mode with 50 or more seconds left.

Silver

Ode To Joystick
Complete Hard Standard Arcade Mode.

On The Tale End
Complete both story mode on Normal or Hard difficulty.

Gold

What's Your Story
Unlock all character story lines on any difficulty.

http://www.ps3trophies.com/forums/trophy-news/55089-acceleration-suguri-x-edition-trophy-list.html