There are 77 armor sets available in Dark Souls III. Some armor pieces do not belong to a set.

Updated guide including locations and armour Sets for Ashes of Ariandel & Ringed City DLCs    • Dark Souls 3 - All Armor Sets Locatio...  

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Timeline:
0:00 - Alva Set
2:38 - Antiquated Set
5:03 - Archdeacon Set
5:34 - Armor of Favor Set
7:33 - Armor of the Sun Set
8:28 - Armor of Thorns Set
11:38 - Assassin Set
12:17 - Black Set
14:52 - Black Hand Set
16:25 - Black Iron Set
18:38 - Black Knight Set
19:02 - Black Leather Set
20:32 - Brass Set
21:12 - Brigand Set
21:47 - Catarina Set
22:40 - Cathedral Knight Set
23:00 - Chain Armor Set
23:31 - Cleric Set
24:00 - Conjurator Set
24:46 - Court Sorcerer Set
25:40 - Cornyx's Set
28:41 - Dark Set
29:02 - Dancer Set
29:34 - Deacon Set
29:54 - Deserter Set
30:14 - Drakeblood Armor Set
32:10 - Drang Set
32:50 - Dragonslayer Set
33:10 - Eastern Armor Set
33:44 - Elite Knight Set
36:18 - Evangelist Set
36:36 - Executioner Set
39:25 - Exile Armor Set
41:46 - Fallen Knight Set
42:10 - Faraam Armor Set
43:57 - Fire Keeper Set
44:27 - Fire Witch Set
44:46 - Firelink Set
45:19 - Grave Warden Set
45:42 - Gundyr's Set
46:41 - Hard Leather Set
47:14 - Havel's Set
49:48 - Herald Set
50:14 - Jailer Set
50:32 - Karla's Set
53:10 - Knight Set
53:41 - Leather Set
56:02 - Leonhard's Set
57:17 - Lorian's Armor Set
58:27 - Lothric Knight Armor Set
58:47 - Maiden Set
59:21 - Master's Set
1:00:01 - Mirrah Set
1:02:15 - Mirrah Chain Set
1:05:20 - Morne's Set
1:07:52 - Nameless King Set
1:08:29 - Nameless Knight Set
1:09:14 - Northern Set
1:10:04 - Old Sorcerer Set
1:10:37 - Outrider Knight Armor Set
1:12:00 - Painting Guardian Set
1:13:03 - Pale Shade Set
1:17:04 - Pontiff Knight Set - Drop from Pontiff Knights
1:17:19 - Prayer Set
1:17:48 - Pyromancer Set
1:19:19 - Sellsword Set
1:20:04 - Shadow Set
1:20:31 - Silver Knight Set
1:20:50 - Smough's Set
1:21:29 - Sorcerer Set
1:22:27 - Sunset Set
1:25:15 - Sunless Set
1:28:19 - Undead Legion Set
1:28:50 - Winged Knight Set
1:29:29 - Wolf Knight Set
1:30:09 - Worker Set
1:30:31 - Xanthous Set
1:32:58 - Clandestine Coat
1:34:17 - Loincloth
1:36:01 - Ragged Mask
1:36:27 - Sage's Big Hat
1:37:18 - Symbol of Avarice
1:38:08 - Scholar's Robe
1:38:40 - Thrall Hood
1:39:14 - Wolnir's Crown