Amethyst is a rarity that is available from level 9.
You can get it as part of rewards for completing Merchant orders or by picking it up from large clay deposits. You can also get amethyst on certain islands when you clear the land of old trees, piles of colored stones, and ruins.
You will need amethyst to upgrade the Stone Poem, and to uncurse the Gate of the Sacred Fifth on Tangled Island. It is also used to craft jewels and dreamcatchers at the Loom.
If you need more help on finding resources in Elf Islands, check out our article Resource Sites!