For full Unicorn taming details, get the taming calculator app.
To tame the Unicorn, you must mount it immediately after the first feeding. Tap the action button each time you're prompted to feed again. Reminder for Mobile players: Your Dododex taming multiplier should always be set to 1.75x for ARK Mobile. Use 17.5x for Soothing Balm.
If it won’t allow you to feed it, knock it out and let it wake up then try again. Most likely due to the fact someone else tried to tame it before. Also, it tells you when to feed it at the bottom corner of your screen. PLEASE UP THIS