Rockster Rocks can be obtained by Rocksters, Rockzillas, Night Rocksters or can be made from Pebble's Pebble - either by killing these creatures or taming them and harvesting from them when they are your Pets.
Rockzillas will only spawn on altars made specifically for them, using at least a minimum of the following: 40 crafted "temple related" blocks - like Obsidian Brick Wall -, 20 natural beach-related blocks - such as Coral, Driftwood, Seashells, or blocks of any part of a Shorewood tree -, and a decent amount of lighting will be required to spawn a Rockzilla.
The aggressive Night Rocksters will only spawn in darkness; not only on Beaches and on Sand, but also in caves and on the Fossil layer underground. Night Rocksters cannot prevail in sunlight, but will burst into blue flames and burn away.
Rockster Rocks are needed as crafting materials for Leather armor.