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