Under the 'READ ME!' heading in the main menu, there is a file called 'STOCKING FILLER'. This file says:
A stocking filler is an extra little present you normally find right at the bottom of your stocking as a token of goodwill.
Or... it is an extra little level you normally find hidden in the last level of your egg as a token of goodwill.
So the secret level is hidden somewhere in the last level of the egg.
Look at the top right corner of the level. There is a christmas tree on the platform up there. If you look very closely at it, you'll notice that there is a spring hiding behind it. Use your balloons to bomb this down onto the light below. Now, move your green duck down to the crowd of orange ducks and use your balloons to make a path over to the spring staircase. Instead of going up this little path, place a balloon under the bottom spring so it falls down slightly. Now, it won't send you up the spring stairway, but instead onto the light. The spring hiding behind the christmas tree is pointing to the right, so you'll need to use your balloons to destroy the thin stack of land in the middle of the light whilst still leaving the spring where it is. This will allow you to be bounced onto the small column at the very right of the screen. The doorway is on there.
Before you do anything in this level, take a look at the situation. You have a group of ducks at the bottom of the screen all separated by nails. The two at the end have presents beside them, but also spikes. If you try to move one duck into a present, all the rest will try to follow him and the duck on the opposite side will hit a spike, killing him and so you'll not be able to complete the level. Therefore, we need to stop them all trying to form a queue. There are two aliens at the top of the level. Bomb a hole so that aliens will fall down and eat two ducks that are sitting next to each other. It does not matter which two ducks, as long as they are ones beside each other. This will create a gap large enough to stop all the ducks from noticing each other, so you can safely move the ducks at the edges into the presents.
A Flying Doctor's Son Production