This is done during Mission 4 when you're tasked with opening a door blocked by a machine and also venting gas out of a room.
In the first area there are -
2 Chest Bursters in glass jars as soon as you enter the room.
7 Eggs (2 burned with a switch, 2 above the medical tables upstairs, 3 more eggs in the middle room downstairs - same room as the face huggers.)
3 Face Huggers (inside glass jars in the middle room downstairs)
In the second are there are -
10 Eggs (2 as soon as you enter that you burn with a switch, 8 in the room with the second switch)
4 Chest Bursters (as soon as you enter the room immediately following the second switch room)
So in total - 26 things you have to destroy. If you don't have this by the time you purge the gas and get ready to go through the next airlock, you've missed something. Go back before going through the next airlock door, otherwise you'll be stuck outside and have to reload a checkpoint.
Edit - Thanks to Pic3k for linking me to a video posted by SKSenior over on YouTube.