Let this serve as a guide to complement Nyxil's solution, which this it based on. The spreadsheet is great to get a sense of what you're missing without spoiling locations, but for those who want more detailed instructions on how to acquire anything, this is for you.
If anything is wrong or any vital information is missing, please feel free to comment and I will edit the solution.
Merchants you will need to find for this achievement:
Merchant Hag Melentia - First encountered next to the second bonfire in Forest of Fallen Giants. After you exhaust all her dialogue here, she will move to Majula the next time you leave the area, where she can then be found sitting by the broken wall near the bonfire.
Carhillion of the Fold - Found on the pier before the boss of No-man's Wharf (take a right at the spot where some enemies climb up onto the pier). When you defeat the boss, he moves to Majula. Go up towards the death monument and turn left to find him sitting on the cliff edge here. Note that you will need at least 10 intelligence before he will sell you spells.
Magerold of Lanafir - When you get to the Iron Keep, turn right as soon as you enter and go to the end of the hallway. Magerold sits on the floor here, and never moves from this spot.
Straid of Olaphis - Petrified in a cell in Lost Bastille, up the stairs from the room on the Bastille side of the bridge to Sinner's Rise. He never moves from this location.
Weaponsmith Ornifex - There are three steps to finding her. First, acquire a Fragrant Branch of Yore and use it on the petrified enemy on the other side of a fallen log from the third bonfire in the Shaded Woods. Killing him will give you the Fang Key. Now continue on to the two towers that you pass between to reach the boss of this area, and go past them. Drop down through the hidden hole that leads down to one of the abyss shrines. Explore this underground area and you will find Ornifex's cell. Unlock it and talk to her, and she will give tell you to meet her at her home. Now go to Brightstone Cove Tseldora, to the area where all the undead mages are shooting at you. On the ground level here is a door which leads to Ornifex's home, and she will be inside, ready to sell to you.
Grave Warden Agdayne - In Undead Crypt, shortly after the room with the mages after the first bonfire. When you get near his room, he will warn you to put out any lights you have with you. Do this, or he will turn hostile. As long as you remain in the dark, he will talk and sell things to you.
Royal Sorcerer Navlaan - You will have to complete a questline for Navlaan in Aldia's Keep before he will sell you anything. You must be hollow to talk to him, and he is found by entering the keep, going to the end of the ground floor and following the hallway right. Going left leads to a lever that releases Navlaan from his cell, so don't pull it. He will give you three tasks before giving you the spell. First, he wants Laddersmith Gilligan's ladder miniature. At this point in the game, Gilligan is most likely sitting by the pit in Majula, where you can just talk to him and buy the miniature. Next, he wants the helm of Cale the Cartographer. If you encountered him in Forest of Fallen Giants, he can now be found downstairs in the manor in Majula. To get his helm, all the flames on the his map need to be lit. To achieve this, just light most of the bonfires and kill all the main bosses. If all flames are lit (which also gives you the Curious About Maps achievement), talk to Cale again and he will give you his gear, incuding the helm. Finally, Navlaan wants the staff of Felkin, the Sunset Staff. Felkin, a merchant right before the first bonfire in Huntsman's Copse, will give you the staff if you talk to him with at least 20 intelligence AND 20 faith. Otherwise, you can kill him for the staff (he is required for some hexes though), or find one in Aldia's Keep by killing the mimic outside, behind the shack with the bonfire. He will now ask for an Aged Feather. Talk to the Emerald Herald when she appears at the start of the Dragon Aerie to acquire one, or just kill her for it. After this, Navlaan will give you Unleash Magic and sell you items and spells. Also not that you actually do not lose the items, you merely show them to Navlaan.
Darkdiver Grandahl - The leader of the Pilgrims of Darkness covenant. You'll have to encounter him in three areas (Shaded Woods, Black Gulch, Castle Drangleic) before he will let you join and sell you things.
Now for the actual spells:
Soul Arrow - Bought from Melentia/Carhillion/Magerold (1500 soul cost).
Great Soul Arrow - Bought from Carhillion/Magerold (3000 soul cost).
Found in Forest of the Fallen Giants. It's on a body on the floor in the room with the ballista ambush, close to where you climb down a ladder and encounter Pate for the first time.
Heavy Soul Arrow - Bought from Carhillion/Magerold (2000 soul cost).
Great Heavy Soul Arrow - Bought from Carhillion/Magerold (4500 soul cost).
Found in a chest in Earthen Peak. If you go to the top floor, where there is a Desert Sorceress on the other side of some broken floor, you can drop down to the right (break the railing) and enter the doorway behind you to find the spell.
Homing Soul Arrow - Bought from Straid/Ornifex (6500 soul cost).
Heavy Homing Soul Arrow - Acquired by trading the Ruin Sentinel Soul with Straid (1500 soul cost).
Homing Soulmass - Bought from Ornifex (6000 soul cost).
Found in Shaded Woods. In a chest right next to the abyss shrine in this area.
Homing Crystal Soulmass - Found in Shrine of Amana. After the third bonfire. It's at the back of the circular area with two sorcerers, on a corpse laying on a fallen pillar. Go behind the pillar to retrieve the item.
Soul Spear - Bought from Agdayne (12,000 soul cost).
Found in Huntsman's Copse. When you cross the bridge with the hollow holding a torch, you'll see a barred up hut on your right. Drop into this hut from the hill above to find the spell on a corpse.
Crystal Soul Spear Acquired by trading the Old Paledrake Soul with Straid (10,000 soul cost). This soul is dropped by The Duke's Dear Freja only in NG+ and onward.
Shockwave - Bought from Carhillion (1800 soul cost).
Soul Spear Barrage - Bought from Carhillion (2500 soul cost).
Soul Shower - Acquired by trading the soul of Scorpioness Najka with Straid (1500 soul cost).
Soul Greatsword - Found in Castle Drangleic. After you climb a long ladder to a room where you charge a golem, the next room has a chest containing this spell.
Soul Vortex - Bought from Agdayne (10,400 soul cost).
Found in Brightstone Cove Tseldora. In the house next to Ornifex's house, with a mage and a spider in it. It's in a chest in a room behind some bookshelves, guarded by a spider.
Soul Bolt - Found in Drangleic Castle. After defeating the Looking Glass Knight, continue past the elevator ahead and turn left to find a chest with this in it.
Soul Geyser - Found in Aldia's Keep. When you get to the long hallway with cages, take the first door on the left. At the bottom of the stairs inside is a cage with corrosive acid (only harms your gear). On a skeleton in the cage is the spell.
Magic Weapon - Bought from Carhillion (2000 soul cost).
Great Magic Weapon - Reward for reaching Rank 1 in the Company of Champions Covenant. Not recommended.
Bought from Navlaan (6000 soul cost).
Found in Black Gulch. In the first open area with lots of poison statues and hand enemies in pools, there's a little cave on the left with a chest containing the spell.
Crystal Magic Weapon - Found in Dragon Shrine, in a chest on a ledge you can drop down to from where you find the Petrified Dragon Egg.
Strong Magic Shield - Bought from Straid/Navlaan (6300 soul cost).
Found in Castle Drangleic. In the room containing "The Embedded" (where you get the key to King's Passage), this is in a chest on the right side of the room.
Yearn - Bought from Carhillion (3000 soul cost).
Hush - Reward for reaching Rank 2 in Way of the Blue Covenant. Not recommended.
Found in Lost Bastille. It's behind a fake wall directly opposite the door to the stairs in the room where you fight the Ruin Sentinels in Lost Bastille.
Fall Control - Bought from Magerold/Ornifex (4800 soul cost).
Hidden Weapon - Reward for reaching Rank 2 in the Bell Keeper Covenant. There are two ways to do this. You can join the covenant in Belfry Luna or Belfry Sol, wear the ring and wait to be summoned, defeat the player and get a win, then repeating this 29 more times. Or, you can do it all by yourself in Belfry Sol. Join the covenant, but don't wear the ring. Climb up from the bonfire, run over to the towers in the back left and look to see if a red phantom wielding two swords has spawned there. If he hasn't, return to the bonfire, rest and try again. He is a somewhat rare spawn, so keep at it. Killing him 30 times and then talking to either bellkeepers will also let you reach rank 2, awarding you this spell.
Repair - Found in Shaded Woods. Right after you go through the Shrine of Winter after getting all the great souls, go down the hill and follow the path to the right to find this on a corpse.
Cast Light - Bought from Straid/Grandahl (3000 soul cost).
Chameleon - Found in Harvest Valley. It's on a corpse in the poison pit with the two big creatures, shortly after the second bonfire of the area.
Unleash Magic - Acquired by completing Navlaan's questline.