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