To complete stage 1-4, you need to use acceleration in a jump – first press the jump and direction buttons (as usual), and then, when you gain enough height, release the jump button and hold down the acceleration button (by default Enter) and hold until you land. This trick will need to be used in the future..
At the very beginning (when you choose which save to play), if you go to the right, you can choose a bonus – a mushroom (costs one life) or a flower (costs two lives). So – if you jump to the rightmost step (in front of which there is a flower), and then jump to the maximum to the right and up, you will find yourself on a secret level. (tested on version 2.16).
At the very beginning of the game there is a mushroom and a flower. Take the flower and go to the very beginning. The very first pipe has a cloud – shoot 3 times into this cloud and you will get life.