There are 44 Trophies that can be earned in this title.

Bronze

Arcade Master
Clear Arcade Mode Ranking Play.

No Rest for the Wicked
Get 500 continual hits in Arcade Mode Ranking Play.

Prologue Cleared
Clear the Prologue in Story Mode.

Stage 1 Cleared
Clear Stage 1 of Story Mode.

Rookie Guard
Clear Stage 1 of Sentry Mode with more than 30000 points.

Veteran Guard
Clear Stage 2 of Sentry Mode with more than 35000 points.

Head Guard
Clear Stage 3 of Sentry Mode with more than 40000 points.

Online Sampler
Play all game modes through Ranking Matches in Online Battle Mode.

Weapon Master
Utilize all Special Weapons through Ranking Matches in Online Battle Mode.

Head of Special Forces
Take down 4 enemies or more in a row without getting killed in a Ranking Match in Online Battle Mode.

Geographical Advantage
Take down 200 enemies or more using G Actions in a Ranking Match in Online Battle Mode.

765
Play 765 or more Ranking Matches in Online Battle Mode.

SCAR of War
Achieve Level 25 through Ranking Matches in Online Battle Mode.

Silver

Jack of All Trades
Unlock all Skills through Ranking Matches in Online Battle Mode.

29 Secret

http://www.ps3trophies.org/game/time-crisis-razing-storm/trophies/