  The Unicorn is a highly elusive creature for four main reasons, it is very fast, it can turn invisible for a short period of time, it flees from Humans, and it is regularly hunted for its horn driving it closer and closer to extinction.
<~><~>  The Unicorn horn is highly valuable for its magical properties. Heed my word, if you come across a unicorn, do not kill it, instead use Shears to clip off the horn, the Unicorn will eventually grow it back.
<~><~>  You can then mash the horn in your Mortar & Pestle to get Crushed Unicorn Horn.