These achievements are all related to earning stars in the game, with the final achievement requiring a total of 500 stars. Stars are earned on a level by surpassing the predetermined score thresholds, with more stars being awarded for higher scores. Score is awarded for destroying blocks, enemies, and objects, as well as for destroying all the enemies with birds left over. There is no way to know the score requirements for one, two, or three stars on a given level. If you are not getting 3 stars, just go for more score, either by using less birds and/or destroying more blocks. There are 630 total stars in the game, and you only need to earn 500 of them. Keep that in mind, as you do not need to earn 3 stars on every level. Earning only two stars on every other level will get you quite close to the 500 needed. Note that stars earned on Bonus Levels, the Awards Room, and the Golden Beachball world DO NOT count towards your total, so do not even bother with them (Thanks to IEvil IMonkey and supadryz for confirming this!). There is no in-game counter for stars. You must manually add them in your head in order to determine your total.
This is the most time consuming task in the game. It is suggested that you stay away from the trial-and-error technique, and go straight to using 3-star video guides to make this as quick and painless as possible. See below for 3-star walkthroughs for all the levels. Thanks to YouTube users WikiGameGuides, AngryBirdsNest, and wicksuper for the videos!