Here is the full list of all 33 Bleed (EU) trophies - there are 12 bronze, 16 silver, 4 gold and 1 platinum.
Recite some poetry atop the Hall of Heroes.
Defeat the Rival with an S-Rank.
Do no damage and take no damage in the Hall of Heroes.
Defeat the Spider Core with an S-Rank.
Investigate the pit in Guppy's Manor.
Defeat the Chopper Core with an S-Rank.
Clear Story Mode on Hard.
Clear Story Mode on Easy.
Win a Challenge Mode fight against 3 opponents.
Defeat the Mirror Core with an S-Rank.
Defeat White Mk II with an S-Rank.
Defeat Guppy with an S-Rank.
Completely trash Guppy's Manor.
Clear Story Mode on Normal.
Defeat the Dragon Heart with an S-Rank.
Defeat Battalion with an S-Rank.
Reach and defeat Bunny Rockette in 3 minutes.
Defeat Bunny Rockette with an S-Rank.
Defeat the Mantis Core with an S-Rank.
Unlock all BLEED Trophies.
Clear Story Mode on Very Hard.
Clear Arcade Mode on Easy.
Clear Arcade Mode on Normal.
Clear Arcade Mode on Hard.
Clear Arcade Mode on Very Hard.
Don't break any egg's in the Earth's core.
Don't trip any lasers in the Hi-Security Complex.
Only fight one color of blob in the underground Lab.
Don't step on the regenerating blocks in the Dragon's stomach.
Reflect a bullet that was reflected by the Rival.
Defeat the Bubble Core with an S-Rank.
Defeat Gibby & Stu with an S-Rank.
Defeat the Laser Bots with an S-Rank.