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