Each level has its own special criteria.
Level 7: Collect the star without hitting a blue brick. You will need to understand the drop technique for this one. Get to the grabber above the star and press up so that you have no side to side momentum and just release down to the star. If you hit a brick at any point, you can use the run as practice or just hit restart level.
Level 8: Collect the star without losing a life. You are probably going to want to do this anyway to help with other achievements, but if you are having trouble, take it slow and avoid all hazards. Don’t worry about finishing under time, or collecting balloons, just focus on getting the star and staying alive. You may have also unlocked the first bonus level, so you can head over there and collect the hidden item for a three hit protection.
Level 9: Collect the star without using a grabber. You can use grabbers after you collect the star, but before that you must avoid them. At the start of the level look at the accelerator to the left. When it takes you away from the cannon, it will shoot you right at the star. Then complete the level, though you are likely to lose a life doing that maneuver.