We can assure you that all levels are tested before they are released, and they are all beatable without making in game purchases. We know it because we, and our testers test them. However, some levels are harder than others, which is what makes the game fun! It all comes down to your strategy and use of explosives.
Try to make matches with more items to get better explosives. You can try to make matches on the bottom side of the board so more items come and this increase the chance for more automatic matches. Of course, making purchases can help you move further faster.