To upgrade your Frozen Egg, you need Frozen Egg Shards.
With each upgrade, you need more Frozen Egg Shards.
Below is a list of possible ways to gain these.
Gems
You can purchase Frozen Egg Shards using gems.
1 Frozen Egg Shard = 15 Gems
10 Frozen Egg Shards = 125 Gems
100 Frozen Egg Shards = 1,154 Gems
1000 Frozen Egg Shards = 10,000 Gems
Chest
You can purchase a chest using guild coins to have a chance at
gaining extra Frozen Egg Shards.
To purchase, click bag, click chests, click the third icon on right hand side.
The chest is called Magical Shard Box and costs 22,500 Guild Coins.
It randomly gives you 10 shards for any of the ruins or statues.