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

Bronze

CLASSIC UFO HUNTER
Elminate all UFOs in Stage 0.

HIGH SCORE OF 10,000,000
Acquire a high score of 10,000,000

1,500 CHAINED
Achieve a chain of 1,500

1,000 NAGOYA ATTACKS
Perform 1,000 Nagoya Attacks in a single stage.

MUSIC FAN
Play Music Mode 10 times.

EASY DIFFICULTY CLEAR
Beat Normal Mode on Easy.

NORMAL DIFFICULTY CLEAR
Beat Normal Mode on Normal.

Silver

HARD DIFFICULTY CLEAR
Beat Normal Mode on Hard.

INSANE DIFFICULTY CLEAR
Beat Normal Mode on Insane.

CHALLENGE MODE CLEAR
Beat all 99 stages in Challenge Mode.

CONTINUE-FREE CLEAR
Beat Normal Mode without using any continues (on any difficulty level with any number of ships).

Gold

NIGHTMARE DIFFICULTY CLEAR
Beat Normal Mode on Nightmare.

http://www.ps3trophies.org/game/space-invaders-infinity-gene/trophies/