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