There are seven secret achievements for the Steam edition of Bleed. There is one for each stage in the game, and they are listed as Secret Mission 01 through Secret Mission 07.
What are the requirements for each of them?
Secret Mission 01: Gate Crasher (Stage 1)
Awarded for smashing all of the chandeliers in Guppy's Mansion
Secret Mission 02: Anti-Omelette (Stage 2)
Awarded for not breaking any of the eggs in the Lava Caves
Secret Mission 03: Lil' Mama (Stage 3)
Awarded for not tripping any of the lasers in the High Security Complex
Secret Mission 04: Speed Demon (Stage 4)
This achievement appears to be awarded for completing the level under a certain time. The exact length of time is not currently known.
Secret Mission 05: Preferred Polarity (Stage 5)
I got this one by not killing any enemies in the first segment of the Top Secret Lab, but the icon seems to indicate that all you need to do is avoid killing any red ones.
Secret Mission 06: Clean Shoes (Stage 6)
Awarded for not landing on any of the membrane inside the Dragon
Secret Mission 07: Perfect Pacifist (Stage 7)
Awarded for reaching the top of the Hall of Heroes without killing any enemies or taking damage
Secret Mission 04: Speed Demon. Acquired by completing the level in a certain amount of time. Most easily done by setting the difficulty to Easy and rushing through the level, not stopping to fight.