Red Dead Redemption (EP)

To find a unicorn you must complete the Undead Hunter Challenges and The Four Horses of the Apocalypse.
Once you have completed those head to east Mexico. The unicorn can be found in the field northwest of Torquemada.
When looking at the map zoomed out it's the spot with the three horse icons.
You will not get the same notice as you did with the other Mythical Creatures.
The Unicorn is very easy to spot though since it leaves a rainbow trail while running and a cloud of butterflies when it's at a standstill.
You have to break the Unicorn once you find it to unlock the achievement.

Hey here is the video I made for you showing you what you have to do and where you have to be to get your Achievement Happy Hunting

To get this achievement you have to break the unicorn. The unicorn will appear in Northeastern Mexico (there are 3 horses on the map where it appears) after you have completed all the other 4 horses of the apocalypse challenges (by breaking each of the four horses and then killing one of each type of undead with the horse Death) and you have completed the Undead Hunter challenges. The unicorn is easily identifiable by the trail of rainbows it leaves while running. Once you break it, the achievement will pop. Good luck. **Note - I killed one of the four horses (pestilence I think), and even after I got Death for completing the undead campaign, I was not able to complete the last challenge. I had to find and break pestilence, so be sure to break all the horses as you find them.

As has been said by the others, the "Fan Service" achievement is for finding and taming/breaking the mythical Unicorn. For the Unicorn to spawn you have to complete all of the Horses of the Apocalypse challenges and the Undead Hunter challenges. I personally found it in Mexico, North West of Torquemada and it spawned seconds after killing the Chupacabra as you can see in the video.

The video also shows me unlocking the "Mad Marston: The Trail Warrior" achievement (for completing all of the challenges) along with the Chupathingy achievement (for killing the Chupacabra).

To find the Unicorn, you must first kill the Chupacabra (for Undead Hunter Rank 5) and find all 4 Horses of the Apocalypse. You will not ever see the Chupacabra until you complete Undead Hunter Rank 4. One of the Horses will be obtained automatically after completing the main storyline. Once you have killed it, head to the large field just northwest of Torquemada (it has 3 horses there on the map). After 1 or 2 runs back and forth across the field, you should see it. It will almost definitely be the only horse you see, and can be spotted more easily than others by the rainbow trail it leaves behind. Then, the standard break, lasso / balance. Now you've broken your very own butterfly-swarming, rainbow-trail-leaving unicorn!

Note: If this horse dies, or you use a blood pact for another horse, you will have to go break it again, as there is no deed or blood pact for the unicorn.

EDIT: Some players have been able to keep the unicorn when it dies, if they have hitched it as their main horse. Note that this is only with some, as others cannot.

I found the unicorn in the same place I found the chupacabra, in the field near Torquemada, on the map when zoomed out it has 3 horses and I found it there.

Make sure to complete Undead Hunter Challenge and Four Horses of the Apocalypse challenge then the horse will appear in the area marked on the video and you shouldn't have much problem finding one. Good Luck.