The Elder Scrolls V: Skyrim Special Edition

To get the achievement you only need to learn at least one word of power for all 20 but you do not have to spend a dragon soul on it so where your points go is up to you.

Of the 20 shouts, 4 can ONLY be learned through the main story, and 4 more can be leaned both in the main story and just by exploring. Once you have visited High Hrothgar you can speak to Arngeir and he will mark the location of a word of power on your map, but he only does this a limited number of times (about 8 for me). You will also periodically receive 'letters from a friend' that serve the same function but they are fairly irregular.

Below is a list of all 20 shouts in the order they appear on your shouts list in the magic inventory. If you're missing one, either go to any of its listed locations, or complete its listed quest. If at all possible, use a location you’ve already discovered before trying to look for these places based on my brief description. Most words are located either at the back of boss room in a dungeon/cave or on top of a dragon’s roost.

Animal Allegiance:
Angarvude – In the mountainside, directly west from Riften.
Ancient's Ascent – East by southeast from Falkreath through Bonechill Passage.
Ysgramor's Tomb – An island northwest from Witherhold. You can only gain access during the Companions’ quest line.

Aura Whisper:
Northwind Summit – Northwest of Shor’s Stone in the Rift
Valthume – Pretty far southeast of Markarth.
Volunruud – South by southwest of Dawnstar on the other side of the mountains where the snow starts.

Become Ethereal:
Ironbind Barrow – South by southeast of Dawnstar, southwest of winterhold on the other side of the mountains.
Lost Valley Redoubt – North by northwest of Falkreath
Ustengrav – Northeast of Morthal

Call Dragon: All three words are leaned during the quest The Fallen.

Call of Valor: All three words are learned during the quest Dragonslayer.

Clear Skies: Al three words are learned during the quest The Throat of the World.

Disarm:
Eldersblood Peak – South by southwest of Morthal.
Silverdrift Lair – South by southeast of Dawnstar
Snow Veil Sanctum – Southeast of Winterhold

Dismay:
Dead Crone Rock – West by southwest of Markarth.
Labyrinthian – Southeast of Morthal. A word of power for Slow Time is found here too.
Lost Tongue Overlook – South of Riften.

Dragonrend: All three words are leaned during the quest Alduin's Bane.

Elemental Fury:
Dragontooth Crater – Directly in between Solitude and Markarth
Statue to Meridia – West of Solitude. This one glitches sometimes I had to go inside the shrine, save, quit, load, and go back outside several times to fix it.
Shriekwind Bastion – Northeast from Falkreath.

Fire Breath:
One word leaned during the quest The Throat of the World.
Dustman's Cairn – In between Whiterun and Morthal
Sunderstone Gorge – North by northwest from Falkreath.

Frost Breath:
Bonestrewn Crest - South of Windhelm
Skyborn Altar - East of Morthal, southwest of Dawnstar.
Folgunthur - Southeast from Solitude.

Ice Form:
Frostmere Crypt – East from Morthal, southwest from Dawnstar.
Mount Anthor – Southwest of Winterhold.
Saarthal – Also southwest of Winterhold.

Kyne's Peace:
Ragnvald – North of Markarth.
Rannveig's Fast – South by southwest of Morthal.
Shroud Hearth Barrow – Right north of Ivarstead at the southeast base of the Throat of the World.

Marked for Death:
Dark Brotherhood Sanctuary – West of Falkreath but you can’t get in without joining the dark brotherhood which starts in Windhelm.
Autumnwatch Tower – South of Ivarstead which is at the southeast base of the Throat of the World.
Forsaken Cave – West by northwest of Windhelm.

Slow Time:
Hag's End – West of Solitude.
Korvanjund – Northeast of Whiterun. You can't enter until you get the quest The Jagged Crown for either the Stormcloaks or the Imperials.
Labyrinthian - Southeast of Morthal. A word of power for Dismay is found here too.

Storm Call:
Forelhost – Southeast of Riften.
High Gate Ruins – Directly in between Dawnstar and Solitude.
Skuldafn – This location can only be reached during the quest The World-Eater’s Eyrie.

Throw Voice:
Shearpoint (all three words together) – Far west of Windhelm

Unrelenting Force:
One word learned during the quest The Way of The Voice.
One word learned during the quest The Horn of Jurgen Windcaller.
Bleak Falls Barrow – Northwest of Riverwood.

Whirlwind Spirit:
One word leaned when you reach High Hrothgar.
Dead Man's Respite – West by southwest of Morthal.
Volskygge – Far west by southwest of Solitude.

I tried to double check all my directions but if you find one that you think is wrong let me know so I can change it.