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