Diamond Eggs are a type of eggs that you can buy for 250 Star Gems, or you could buy them in bulk (6 eggs) for 1000 Star Gems. The 6-pack bulk is the highest-priced item in Outernauts as of May 17, 2013, worth $100 in US dollars.
Diamond Eggs hatch only epic or legendary beasts. The latter has a high chance of appearing, as the 6-pack says that it "guarantees that you'll get at least 1 legendary beast with it, unless you have the luck of a no-leaf clover".
The beasts hatched also have better gem and metal types.