Hi, it's been almost 2 years now, but I researched the issue and recreated the situation from your question (I started the quest on new character and after creating the Beaver Cure I threw it into dustbin). Here are my conclusions, I hope it's gonna be useful to others who may have encountered the same problem as you :)
Q: Does anyone have any idea how to get this item again?
A: To get this item again, just reproduce the following steps from Within the Tides Quest:
- Get the Coral Branch (you can buy it on market or loot it from Foam Stalker) and collect the Moon Mint again (it can be harvested from Moon Mint plant here. The flower respawns every few seconds).
- Go to the laboratory (here) and use the Coral Branch in the Mortar and you'll obtain Coral Powder.
- Go east and use your Moon Mint and Coral Powder in the Refiner of Magic. If you have done it correctly you will obtain the Cure for Sick Beavers again and you can continue doing quest.
Q: Is there an Npc that sells the item?
A: No, there is no NPC who sells this item.
Q: Is there a keyword that must be spoken to an npc to obtain the item?
A: No, you just have to prepare the item again.