These achievements just require you to complete all levels with three stars. You get an achievement for completing a single level with 3 stars, and each of the 4 worlds with 189 stars (63 levels per world x 3 stars per level). The levels are quite easy and can quickly be completed without a guide. World 4 (Frozen Mellow) has some trickier puzzles that using a guide would definitely save time on, but overall the levels are much, much easier than Fragger if you played that. They require much less precision and timing.
To get three stars you basically just have to get a certain score. This mostly just boils down to completing the level using the minimum number of objects (stones/bombs). However, because some of the objects have different points awarded for not using them, it is sometimes required that you use specific types of objects.
THIS SITE has some good walkthroughs for each level. However, simply typing in the World name and level number into YouTube is just as good. There are numerous walkthrough videos for each level. To me, at least the first two worlds, it is definitely faster to just play without guides. They can actually slow you down as most levels only require mild thought and can be completed in one attempt.