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