Here is the full list of all 25 The Penguin Factory achievements.
Complete the game
Deliver 1,000 penguins
Deliver an imposter penguin by mistake
Send 500 penguins through splitters
Send 1,000 penguins through tubes
Send 1,000 penguins onto turntables
Hit 100 imposter penguins with mallets
Hit a genuine penguin with a mallet
Turn 1,000 conveyor belts on or off
Change the direction of conveyor belts 500 times
Change the direction of splitters 100 times
Turn 100 mallets on or off
Turn 250 tubes on or off
Turn 100 turntables on or off
Change the direction of 250 turntables
Collapse 500 platforms
Complete a level with less than five seconds remaining
Use a mallet to hit one penguin into another penguin
Complete level 57 with at least two direction changes to spare
Complete level 60 within 30 seconds
Complete level 77 having switched the splitter before starting the conveyor belts
Complete level 19 with at least one direction change to spare
Complete level 40 with a single swing of the mallet
Complete level 82 having turned off only five turntables
Cause a penguin pile up!