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