There are 12 Trophies that can be earned in this title.

Bronze

UNLOCK ARCADE STAGE SELECT MODE
Unlock ARCADE MODE Stage Select: Complete a single-player ARCADE game in 13 PLANE MODE.

UNLOCK EXTRA STAGE SELECT MODE
Unlock EXTRA MODE Stage Select: Complete a single-player EXTRA game in 13 PLANE MODE.

UNLOCK 13 PLANE MODE
Unlock 13 PLANE MODE: Complete a single player game in ARCADE MODE and EXTRA MODE.

R-GRAY0 ROLLOUT
Unlock R-GRAY 0: Complete a single player game in ARCADE MODE.

R-GEAR ROLLOUT
Unlock R-GEAR: Complete a single player game in EXTRA MODE.

UNLOCK RATE VIEWER
Unlock Kill Ratio Display: Complete a single player game in either ARCADE MODE or EXTRA MODE of 13 PLANE MODE.

UNLOCK UNLIMITED CREDIT
Unlock Unlimited Credits: Use a total of 50 credits in single player games.

Silver

OVERALL LOCKON AVERAGE 80%
80% Lock-on Average: Complete single player game in any mode with an average lock-on percentage of 80% or more in every stage.

OVERALL SHOOTINGDOWN AVERAGE 80%
80% Kill Ratio Average: Complete single player game in any mode with an average kill ratio of 80% or more in every stage.

LOCKON DOWN 10000 UNIT
10,000 Total Lock-on Kills: Achieve 10,000 total lock-on kills in single player games.

SHOOTINGDOWN 15000 UNIT
15,000 Total Kills: Achieve 15,000 total kills in single player games.

Gold

NO CONTINUE CLEAR
No Continues Completion: Complete any mode besides 13 PLANE MODE without continuing in single player games.

http://www.ps3trophies.org/game/raystorm-hd/trophies/