For this achievement you will have to finish every level with all Raydians liberated, which basically means you have to paint them by touching them. Some will be lying around on the ground or platforms, others will come out of their houses once you've painted an entire block of houses etc.
You can check the progress in a level by pausing the game, selecting 'PROGRESS' and then selecting the Raydians medal.
Tip from coldraught:
To check the status on all of the levels, you can find the information by going to menu - extras - awards and scrolling through all of the awards for each level.