These achievements are unlocked by completing all 30 levels in each of the 7 worlds of the game. Completing a level only requires that you destroy all of the enemies or free all of the birds from their cages (depends on the world). The first level of each world is unlocked from that start. Subsequent levels in each world are unlocked by completing the previous level.
Achieving a given number stars or score does not matter for these achievements. However, you should at least attempt to earn two stars on every level to work towards a total of 500 stars for the star-related achievements. See "Stellarvore" for links to 3-star walkthroughs for every level if you are stuck.