The lower cluster only contains three eggs, so you should focus on getting to these as quickly as possible. Spread your attack, throwing a different color of bubble to each of the three areas near where the eggs are. Try to pop / burst each egg as soon as you can.
For the upper level, spread your attack in the same way, being sure to clear bubbles from all the way around the lower edge of the cluster. Note that it is not necessary to burst egg bubbles which do not contain babies. Focus on the egg bubbles which also contain babies.