ARK's base taming speed on PC, PS4, and Xbox is now doubled, meaning 1× is as fast as what 2× was previously. Dododex has been updated to reflect this. Use the "presets" dropdown for common multipliers.
For full Unicorn taming details, get the taming calculator app.
Taming Calculator (Passive)
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. On ARK: Mobile, you can only use Griffin Kibble. Reminder for Mobile players: Your Dododex taming multiplier should be set to 0.875x for ARK Mobile. You can use Settings presets for ARK Mobile and Soothing Balms.
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.
I encountered one on Ragnarok, freaked out tamed it and was happily riding it back to my base when a stupid Raptor decided "I'm about to ruin this man's career" and killed my Unicorn. I have yet to find another one and I have a gravestone for my lost Charlie.