There will be spoilers. Be warned.


What you need to do to get the following acheivements:

Beginning Light - Simply start playing lucy.
Abandoned Robot - Unlocked as soon as you find lucy at the dumpsite.
Adventure Gamer - Unlocked by clicking on the room multiple times instead when prompted to examine lucy. The password that you get can be used to unlock the extra CG section if you start a brand new game with clean data. You go to the extra section and click the jumbled text, then enter the password. Though I did not find any unlocked CG's, it's still blank.
Faster than Light - You click the words 'Lucy' in the main title screen after completing the games true end.
Reckless Challenge - Select the option to try and put lucy into a bag.
Chivalrous - Say that lucy is heavy when she asks.
Reliable Source - Say that the food tastes horrible.
Butterfly Effect - Keep the flyer the repairman gives you.
Cendrillon - Help lucy do the laundry.
Place of recollection - Look for her and when given the choice to either return or keep searching, choose keep searching.
Dream of Electric Sheep - You do not seem to need to have found lucy on Oct 21 to get this.
Forgotten memory - During the epilogue, choose 'I regret it'
Unto Eternity - During the epilogue, choose 'I don't regret it', then play Oct 12 which replaces the start button. If you want to play this scene again after completion, it appears you have to either load a save or choose 'I don't regret it' and pass the credits again.The start button will then be replaced with Oct 12 again.
Reunion - Will be unlocked when you've played 'old mans wish' that is unlocked after completing the game and/or played 'Reunion' that is unlocked after reaching the true end. Reunion appears to replace 'Old man's wish' if you've obtained the true end.
Hidden Diary - Unlocked after seeing Dr. Baek's Log, which is unlocked after completing 'Reunion'

(This is how I got the acievements. Sorry if it is not clear. I'm sure someone will make a better one in the future, for now use this guide.)