To upgrade your Horned Altar, you need Horned Altar Shards.
With each upgrade, you need more Horned Altar Shards.
Below is a list of possible ways to gain these.
Gems
You can purchase Horned Altar Shards using gems.
1 Horned Altar Shard = 15 Gems
10 Horned Altar Shards = 125 Gems
100 Horned Altar Shards = 1,154 Gems
1000 Horned Altar Shards = 10,000 Gems
Chest
You can purchase a chest using guild coins to have a chance at
gaining extra Horned Altar 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.