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