An easy way to earn eggs is to play Multiplayer because even if you come in last you will still earn some.
It is more beneficial to progress slowly through the game and explore the courses as doing so will improve your chances of finding the 'ghost flag' which is hidden on one map within each course.
Flying Straight Up:
You will be able to fly up in a straight line by alternately tapping on the left and right flap buttons. There will be times when you will need to be able to do this.
Try scrolling up if you are having difficulty finding the last few eggs for a course as there is a good chance they may be in the sky above you just out of view.