If you don't mind cheesing it, you can earn this easily doing the Dragonborn DLC, and you'll need 11k gold.
1.) Play the story until you are summoned by the Greybeards, and acquire the horn, and finally return to the Greybeards, being fully recognized as Dragonborn.
2.) Run around until you are accosted by some cultists who look like they have a Cathulu mask. Answer them, doesnt matter what you say. Kill them and loot their corpse for a note.
3.) Head to Windhelm, then to the docks for passage to Solthesiem, when able, head South-South East to find Kolbjorn Barrow. You'll run in to Ralis, who asks for some money, agree.
Steps 4 and 5 in more detail
4.) Fast travel back to Raven Rock, and while inside, wait for 48-60 hours. Go outside and a courier will give you a note to return to Kolbjorn. Talk to Ralis, and kill Draugr.
5.) Repeat until you deal with Ralis. In the area you fought the Dragon Priest, continue through the crypt to find a Black Book.
6.) At the end of the bool, select "Secret of Arcana", a Power that reduces mana cost to 0 for 30 seconds.
7.) You now need the spell Telekenesis. This can be acquired easily at Benkongerike, which can be found on Solthesim, to the southeast of Saering's Watch (a Dragonborn DLC plot location) or to the northwest of the Headwaters of Harstrad at about the halfway point between both locations.
Just after entering Benkongerike Great Hall, to the right, in a tent, is a pile of thirteen copies of The Lusty Argonian Maid Vol 1 and six copies of The Lusty Argonian Maid Vol 2, and under these books is a Spell Tome for Telekinesis.
8.) NOW, with "Secret of Arcana" as your Power, and Telekenesis equipped, find an item, use your Power, and use Telekenesis. While using Telekenesis, bring up the map and fast travel. As far as you can (you can do this in Skyrim, usual Riften to Dawnstar or vice versa is fine). This will raise your Alteration to 100.