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