At the moment, there seem to be 13 armor sets that work for this achievement. A few of the sets can be obtained in any campaign, but some require optional dungeons that may or may not be present in a given playthrough. If you don't have the required dungeon, you'll have to reroll your campaign or start a new adventure and hope for the best. You can also join someone else's game and hope they have the dungeon / event. Since you need to join other people's games for the 30 trait achievement anyways, I'd recommend trying this.
Whatever archetype you start with will grant an armor set for free. As far as I can tell, this starting set will not count towards the achievement. Obtaining the other starting sets will count when you buy them during the campaign.
It should also be noted that the tracker on the Xbox achievement list did not seem to update properly if a set was gained in a multiplayer game. Don't worry, it still counts. However, it might be best to get your last set in a single player game, just to be safe.
Last fun fact about armor sets: each armor set comes with a bonus of some sort when worn, with the bonus being larger the more set pieces you wear. The bonuses can be found by inspecting the armor in your inventory. Equipment can be upgraded like weapons at Rig's in Ward 13.
Every game sets (5 and a half towards achievement)
Adventurer Set (doesn't count for achievement)
- Obtain: Prologue armor. Only shirt and pants.
Cultist Set
- Obtain: Starting armor for ex-cultist archetype. Alternatively bought from Rig's store in game at Ward 13 for scrap
Hunter Set
- Obtain: Starting armor for hunter archetype. Alternatively bought from Rig's store in game at Ward 13 for scrap
Scrapper Set
- Obtain: Starting armor for scrapper archetype. Alternatively bought from Rig's store in game at Ward 13 for scrap
Void Set
- Obtain: On Rhom, you'll find a sub region called the "Monolith". Right in front of this crystal, there is a metal plate in the ground, with four symbols on each side, like a compass. Now, looking at the Monolith, go around the right side of the tower until you get to the back. On the Monolith tower itself, there will be a sequence of those symbols scratched onto the tower. Write these down - they change from campaign to campaign. Now go back and, starting on the metal plate, you'll see stone floor squares surrounding the plate. Walk using the pattern you wrote down. If you're doing it right, the stone you stand on will sink into the ground and stay down. Partway through the puzzle, enemies will spawn, so be prepared to hold your ground - don't move off onto a wrong tile. This might happen a couple of times. Also, if you move onto a wrong tile, all the tiles will raise back up and fairly powerful enemies will spawn, with enemies getting more powerful with the more wrong attempts you make. After you complete the puzzle, the metal tile that you started from will sink / slide away revealing a hole. Drop into the hole, and walk up the stairs to a console in front of the door. Use the console to craft the void armor set. 2,500 scrap required.
Slayer Set
- Obtain: Accept the Undying King's Quest and travel to Corsus. On this planet, there is an NPC called the Elf Queen or the Swamp Queen. She is found in a hut next to a crystal sub-region appropriately called "The Elf Queen". Talk to her and she will also ask for the heart. Go kill the world boss and get the Guardian's Heart. Travel back to The Elf Queen and choose to give the heart to her instead. She will give you this set and a crossbow for doing so. Then go kill the King for another achievement and trait.
Ossesus Set
- Obtain: On Rhom, there is a merchant called Wud. He is in the Scouring Wastes sub-region, behind a locked door. You have to first go through a dungeon to be able to enter the backway, and open the door. He has a lot of nice things in his shop. He also offers to sell you secrets for 100 scrap each. Buy all the secrets - he'll eventually run out. After buying all his secrets, he'll offer to sell you this set of armor in his store. Buy the armor.
Drifter Set (only partially available every game - helmet location in random chance section)
- Obtain: The pants and torso armor are found in the very first area after Ward 13, in the Founder's Hideout. This is the place you get the keycard. On the wall is a corpse, and to the left of the corpse is a bookshelf. Break the bookshelf. There is a secret area behind it - crouch and walk through. This area has the torso and legs for the Drifter Set on a display in this small area.
Random chance armor
Drifter Set (helmet for completion)
- Obtain: Drifter helmet, if it shows up, will show up on Earth. It will be lying next to a corpse in either one of the overworld regions, or in one of the dungeons. As far as I can tell, it's spawn is not guaranteed, and is competing with the other 6 purple Earth drops and quest item drops (coin and ring). If you roll campaigns / Earth adventures and search Earth enough, eventually it will drop. It appears that one tome and one random drop appears in each zone / most dungeons (Fairview, Westcourt, Chapel Station, etc.), so happy hunting.
Bandit Set
- Obtain: First off, you have to have visited Mud Tooth's Hideout on Earth and gotten the pocket watch. His hideout, if it spawns, is not a dungeon, but a checkpoint in above ground zone. It competes with the Settlement and the Wailing Wood checkpoints for spawn. If you have Mud Tooth's Hideout, you'll notice a big air cargo plane wrapped up in a tree and likely hear Mud Tooth talking to himself. Walk up through the back of the plane to talk to Mud Tooth. Listen to all his stories. At the end, he'll give you a pocket watch (amulet). With this amulet, you now need to find a dungeon on Earth called "Cuttthroat Channel". If this dungeon spawns, it will be in Westcourt, in the north, and will be a sewer entrance, not cave or tunnel. At the end of this dungeon, you'll reach a location called "The Depot", where you normally have to fight a boss called Barbas. However, if you have the pocket watch, you can choose to give it to him instead. If you do so, you will receive the Bandit set and skip the fight.
- Special Note: There is also a trait linked to this dungeon in multiplayer called "Cold as Ice". You will likely not be able to get both trait and armor set in same run, and the trait is rare because of the steps needed. You'll need to look up steps for the trait.
Leto's Set
- Obtain: The dungeon you're looking for is on Earth and called "Research Station Alpha". You're in the right place if you get a quest to escape Leto's lab. The entrance will be in an abandoned building, at the bottom of some stairs, probably at the north of the map. Play through the dungeon until you get to the iron teleportation chamber (you'll need to use the computers throughout the place to lift bypass and activate security protocols and fight monsters). When you get to the chamber, there will be a computer directly across from it. The computer will ask if you want to disable Leto's Algorithm. For this set, you want to disable the algorithm - you'll probably have to re-enable to proceed through the dungeon afterwards. After disabling, step into the chamber. You'll be teleported to one of a few of different random locations. You'll likely need to repeat this step a few times, until you get teleported into a room with a mini-bonfire of human remains and probably a couple of enemies. In a little side room from here, the armor set is on display. Walk over and grab it before going up the stairs and unlocking the door back to the chamber. Side note: for the boss of this dungeon, I recommend the Hive Cannon for its AoE effects, if you have it. It's a hard boss.
Twisted Set (full set plus extra helm)
- Obtain: The dungeon is on Earth and called "The Gallows". It will be a tunnel entrance and either to the east or south of the checkpoint in Westcourt region. It's a pretty simple event called "The Root Shrine". Go through the fog and survive the waves of enemies. At the end of it, you can go to the base of the tree in the center and there is a root crafting table. Craft the set here using scrap.
- Extra head piece (likely not required for achievement, but used for a trait): There is another head piece that uses the same bonuses as the other armor pieces in this set. It is found in the earth dungeon called "Junk Town". This dungeon can spawn in either Fairview or Westcourt regions. It has no enemies, except a merchant at the end. Buy his stuff ... then ask about his mask. Keep asking about it until he gets angry and attacks you. Kill him, get the mask. You can wear this mask and talk to the Wailing Tree (if the checkpoint spawns in one of your Earth overworld zones). If you do so, it will give you the trait "Bark Skin".
Akari Set
- Obtain: This set is found on Rhom. The dungeon is called "Vault of the Herald". I believe it is a random dungeon, so it may not be in your playthrough, but I have seen it a lot. Before you start searching for the dungeon though, you need to find a couple of quest items called "Glowing Rod". They are lying on the ground in the other dungeons of Rhom. You need a total of three of them to get the full set of armor. One rod will be found in the Vault of the Herald dungeon itself, so you really need two others, which are found in the other boss dungeons in the world. The Ardent Temple, Burrows and Shackled Canyon, are ones that I know has a rod inside. Once you get all three rods, you will need to fight your way to the end of the Vault of the Herald. At the end of this dungeon, there are three pedestals. You need to insert a rod into each pedestal. For each rod you insert, a door in front of the pedestal will open and the door will have a piece of the armor. I believe that the armor and door position are fixed, so the left door will always have the helm, the middle the torso piece, and the right has the leggings, in case you can't find all three rods and have to roll another world. Since the vault itself seems to guarantee one rod, you can just find the dungeon and get the piece you missed.
Elder Set
- Obtain: On Yaesha. The dungeon you want is called Temple of the Ravager. At the end, you will enter a place called "Martyr's Sanctuary" and pass through a fog wall. At the end there is a door. Approach the door, and an event begins called "Survive the Attack". So...survive the, uh, attack. Once the door finishes opening, walk through to find the Elder Set.
Radiant Set
- Obtain: On Yaesha. First you have to find the Stuck Merchant. If she spawns, she will be in the overworld and will have her own checkpoint. You'll need to buy the torso and legs from her. Make sure to do this before getting the helm (described later). If you don't buy them, you'll be locked out of the torso and leggings until you roll another world because she dies. She also has a cart next to her with an item called a "Strange Curio". Grab the item. You then need to use the Strange Curio in the Merchant Dungeon to open the door. This dungeon isn't necessarily next to the stuck merchant, explore your world. It's an underground cave. After using the curio on the big statue door, you'll find a tome on a pedestal in this room. Grab the tome. It will spawn a boss called the "Root Horror". You just need to get it down to 50% and it will leave. The helm will then be found to the left of the pedestal that had the tome.
- Special note: After you get the helm, when you go back to the merchant location, the Root Horror boss will be there and will have killed the merchant. Finish killing the boss here to get a trait called "Guardian's Blessing".