There are 3 ways you can get this achievement. One is 1500 crowns (real money currency), second is having someone who is currently a Vampire bite you. This requires them to be level 6 in the Vampire skill line and have the ability unlocked. Third is to get bit yourself, please see SaucySlingo's maps as they are correct, and do the Scion of the Blood quest line.
What you have to do is go to one of the spots on the maps Saucy provided and get bit by one of the bloodfiends that are there. It can only be at night however you can get bit in any of those spots, it is not faction specific I can personally confirm this. You will know if you contracted Vampirism because it will show as an active effect when you look at your character.
After that you must find the quest giver for the Scion of the Blood. I know there is a quest giver in each of the faction areas, The Rift, Reaper's March, and Bangkori. I have attached a screenshot of where the quest giver is in Reaper's March. He is leaning up against the fence on the right side if you come in from the south entrance of Rawl'kha.
Talk to him and you will start the Scion of the Blood quest. You will have 2 choices, make sure you do NOT visit the healer as she will cure you of Vampirism. Below is where the crypt you will need to go to in order to become a vampire and get the skill line unlocked. I marked it with a custom waypoint on the map.
As soon as you complete the quest, the skill line will unlock and you will be a vampire and get the achievement.
As a side note, I don't know if the quest line is faction specific, the screenshots are for the Aldmeri Alliance in Reaper's March, or if any faction can use this to start the quest. If someone who is in a different faction uses this guide and can confirm whether or not he can start the quest in Reaper's March I will update this solution to say so.