Get the Ring of Hircine as it will allow you to transform as often as you want as oppose to once a day. I got 9 feedings just on this quest - you have to agree to kill the hunters and not who Hircine sent you for. You have to equip the ring after each transformation because all of your gear is unequipped - making the ring a favorite will help. From there it is just a matter of killing and feeding until you get enough to earn the perks.
5 feeding - 1st perk
7 more feedings - 2nd perk
8 more feedings - 3rd perk
9 more feedings - 4th perk
12 more feedings - 5th perk
14 more feedings - 6th perk
16 more feedings - 7th perk
18 more feedings - 8th perk
20 more feedings - 9th perk
22 more feedings - 10th perk
24 more feedings - 11th perk
There are 11 perks so you will need to gain all of them which is 155 feedings.
To feed you need to get close to a corpse, you do not have to have been the one to kill them, and a prompt to press (A) (If using controller) will appear to feed - this will extend your Bloodlust and allow you to stay a werewolf for longer. The savage feeding perk allows you to feed on most dead creatures - making it easier to get the required kills - all the way right on the skill tree. There are a few things you cannot feed on: Vampires, Skeletons, Draugr, Spriggans and Dragons.
Some good places to feed are Stormcloak forts - I would suggest fast traveling first because the map is not available to you when you are a werewolf. Also, I've been told that northern Skyrim has lots of easy prey like wolves and such - thanks Malicious. I just ran from quest to quest as a werewolf hunting deer and other animals.
~ READ THIS IF YOU'RE HAVING TROUBLE TURNING BACK INTO A WEREWOLF. ~
So here is why this achievement is missable, Aela the Huntress is the ONLY person in all of Skyrim who can change you back into a werewolf. But if you have finished the Companion's quest line and cured your Lycan disease you might have trouble with this achievement.
After you finish the Companion's quest line you can marry Aela the Huntress, If you chose to marry her then she is no longer invincible and can die. If she dies and you cure your werewolf disease then you can never become a werewolf again.
There is a rumour that if you wait a month (In-game time) then she will respawn, but I tested this myself and waited 37 days and she never came back from the dead.
So basically If you have finished the Companion's quest line and cured your Lycan disease and Aela the Huntress is either dead or missing, then you will need to start a new save.
It might be possible to find a random Lycan running around and get bit and become a werewolf but I could never find any.
If you find this solution to be unhelpful, please tell me why in a comment and I will update it the next time I'm online.