I believe the file you need to copy and paste is located at:
X:\Documents and Settings\Owner(or whatever you have it called)\Local Settings\Application Data\Ironclad Games\Sins of a Solar Empire\Setting\achievements.achievements
Make sure you have the 'show hidden files' option checked in Tools -> Folder Options -> View
Transfer that to the same location on the other computer and you should be in business. If transferring the file isn't the easiest option for others, you can also open that file with Notepad or Wordpad and just change the ones you know you received from FALSE to TRUE.