Tortoiseshell Fragment

 are crafting materials that are dropped by Dragon Tortoise and are used to craft Tortoiseshell Aegis.

In order to get the 50 materials needed to craft the armor you need to defeat the boss up to tier #15. In order to gain the additional 50 materials needed to craft the plus version of the armor you need to defeat the boss up to tier #43.

This material can also be obtained by summoning the epic boss at the Summoning Stone. If the Boss is active, it will cost 11 gems; otherwise, it will cost 30 gems.