Here is the full list of all 32 Bleed achievements.
Clear Arcade Mode on Easy (or higher).
Clear Arcade Mode on Normal (or higher).
Clear Arcade Mode on Hard (or higher).
Clear Story Mode on Hard (or higher).
Clear Story Mode on V. Hard.
Recite some poetry atop the Hall of Heroes.
Clear Story Mode on Easy (or higher).
Clear Story Mode on Normal (or higher).
Defeat the Rival with an S-Rank.
Reflect a bullet that was reflected by the Rival.
Defeat the Dragon Heart with an S-Rank.
Defeat the Bubble Core with an S-Rank.
Defeat Battalion with an S-Rank.
Defeat the Mirror Core with an S-Rank.
Defeat the Laser Bots with an S-Rank.
Investigate the pit in Guppy's Manor.
Defeat the Chopper Core with an S-Rank.
Win a Challenge Mode fight against three opponents.
Defeat Bunny Rockette with an S-Rank.
Defeat the Mantis Core with an S-Rank.
Defeat White Mk II with an S-Rank.
Defeat the Spider Core with an S-Rank.
Defeat Gibby & Stu with an S-Rank.
Defeat Guppy with an S-Rank.
Clear Arcade Mode on V. Hard.