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