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