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