Here is the full list of all 39 Bio Prototype achievements.
Defeat a Boss
Defeat 5000 Monsters
Defeat 20000 Monsters
Defeat 50000 Monsters
Unlock 4 sets of Brain
Have 8 Life
Complete a game with Stomy(Stage 1 or above)
Complete a game in Stage 1
Complete a Wave without killing any monster
Link 3 different types of Offspring
Complete a game with Genius(Stage 1 or above)
Complete a game with Nature(Stage 1 or above)
Complete a game with Hydra(Stage 1 or above)
Complete a game with Queen(Stage 1 or above)
Complete a game with Squander(Stage 1 or above)
Complete games with 10 different Prototypes(Stage 1 or above)
Complete a game in Stage 2
Complete a game in Stage 3
Complete a game with Hunk(Stage 1 or above)
Complete games with 3 different Prototypes(Stage 1 or above)
Complete a game with Wealth(Stage 1 or above)
Upgrade 3 different projects to maximum level in Culture Room
Complete a game with Sheep(Stage 1 or above)
Link 8 Organs in a set of Brain
Link a Belly and a Poison Bag to the same Brain
Defeat a Boss while you are buffed by Wings
Pick up 2000 Cells
Link Limbs to 4 different Brains
Complete a game in Stage 5
Complete a game with only one brain (Stage 1 or above)
Complete Wave 25 in Endless Mode
Complete Wave 35 in Endless Mode
Install 3 Horns in a Brain
Defeat a Boss while you have only 1 HP
Complete a game with Fate (Stage 1 or above)
Complete a game with Rhinoceros (Stage 1 or above)
Complete a game with Harmony (Stage 1 or above)
Complete Stage 5 with 3 different Prototypes