There's lots of armor throughout the game, with the best armor also being the most time-consuming to obtain, requiring multiple sets of Hardmode armor. Hardmode armor includes three different types of helmets for each set as well, and you'll need to craft them all for use as materials for the best armor.

This achievement is finicky and may not unlock once you've collected everything. Shuffling your armor around in chests and in your inventory or dropping it and picking it back up should cause it to pop.

Mining Armor Mining Helmet, Mining Shirt, and Mining Pants. You buy the Mining Helmet from the Merchant for 8 gold. The shirt and pants are rare drops from the Undead Miner and Vampire Miner, zombie-type mobs found in the Cavern layer. Depending on luck, this may be the last set you complete. These already rare mobs are even more scarce once you unlock Hardmode, so make a new world instead when you plan on farming them.
Copper Armor Copper Helmet, Copper Chainmail, and Copper Greaves. Requires 60 Copper Bars to craft the entire set.
Iron Armor Iron Helmet, Iron Chainmail, and Iron Greaves. Requires 75 Iron Bars to craft the entire set.
Silver Armor Silver Helmet, Silver Chainmail, and Silver Greaves. Requires 75 Silver Bars to craft the entire set.
Gold Armor Gold Helmet, Gold Chainmail, and Gold Greaves. Requires 90 Gold Bars to craft the entire set.
Meteor Armor Meteor Helmet, Meteor Suit, and Meteor Leggings. Requires 75 Meteorite Bars to craft the entire set.
Jungle Armor Jungle Hat, Jungle Shirt, and Jungle Pants. Requires 12 Stingers, 2 Vines, 32 Jungle Spores, and 1 of each type of gem (Diamond, Ruby, Emerald, Sapphire, Topaz, and Amethyst).
Necro Armor Necro Helmet, Necro Breastplate, and Necro Greaves. Requires 150 Bones and 135 Cobwebs to craft the entire set.
Shadow Armor Shadow Helmet, Shadow Scalemail, and Shadow Greaves. Requires 50 Demonite Bars and 45 Shadow Scales to craft the entire set.
Molten Armor Molten Helmet, Molten Breastplate, and Molten Greaves. Requires 90 Hellstone Bars to craft the entire set.
Cobalt Armor Cobalt Helmet, Cobalt Mask, Cobalt Hat, Cobalt Breastplate, and Cobalt Leggings. Requires 45 Cobalt Bars to craft a set, 65 Cobalt Bars for everything.
Mythril Armor Mythril Helmet, Mythril Hood, Mythril Hat, Mythril Chainmail, and Mythril Greaves. Requires 45 Mythril Bars to craft a set, 65 Mythril Bars for everything.
Adamantite Armor Adamantite Helmet, Adamantite Mask, Adamantite Headgear, Adamantite Breastplate, and Adamantite Leggings. Requires 54 Adamantite Bars to craft a set, 78 Adamantite Bars for everything.
Hallowed Armor Hallowed Helmet, Hallowed Mask, Hallowed Headgear, Hallowed Plate Mail, and Hallowed Greaves. Requires the Cobalt, Mythril, and Adamantite Armor sets, 20 Soul of Might, 20 Soul of Fright, and 20 Soul of Sight to craft a set, with 40 more Soul of Sight to craft the other two helmets.
Dragon Armor Dragon Mask, Dragon Breastplate, and Dragon Greaves. Requires the Cobalt, Mythril, Adamantite, and Hallowed Armor sets, 60 Souls of Might, and 60 Souls of Blight to craft a set. Needs the "melee" version helms (Cobalt Helmet, Mythril Helmet, Adamantite Helmet, and Hallowed Mask) from the other sets to craft. All pieces have a chance to drop from Ocram.
Spectral Armor Spectral Headgear, Spectral Armor, and Spectral Subligar. Requires the Cobalt, Mythril, Adamantite, and Hallowed Armor sets, 60 Souls of Blight, and 60 Souls of Fright to craft a set. Needs the "caster" version helms (Cobalt Hat, Mythril Hood, Adamantite Headgear, and Hallowed Headgear) from the other sets to craft. All pieces have a chance to drop from Ocram.
Titan Armor Titan Helmet, Titan Mail, and Titan Leggings. Requires the Cobalt, Mythril, Adamantite, and Hallowed Armor sets, 60 Souls of Blight, and 60 Souls of Sight to craft a set. Needs the "ranged" version helms (Cobalt Mask, Mythril Hat, Adamantite Mask, and Hallowed Helmet) from the other sets to craft. All pieces have a chance to drop from Ocram.
Note: The Wizard Hat does not count.

Strategy for Mining Armor: Dig down to the lowest part of the Cavern layer (just above the Underworld) and find a good-sized natural cavern that extends horizontally a few screens. Skeletons spawn at an increased rate at this level, which increases your chance of getting an Undead or Vampire Miner. Fill in any other empty pockets around your main cavern to prevent enemies from spawning there. Cover up any lava pools. Now stand in the middle and wait for enemies to come to you. Using a Battle Potion and Blue Candle is recommended, but not necessary. This method also works for getting a Pinky to spawn.

Strategies for farming materials: Souls aren't rare, but you need plenty of them for the boss summoning items and Hardmode armor. Here's a link to the method I used for Souls of Light/Night.

I never had enough Lens when I needed them for The Twins, so here's a magnificent video for farming them:



Note: Create your Lens farm in Normal Mode.