This is a very straightforward achievement, as it is explained in the title description. You have three weapon slots, and five armor slots. There is also a slot for your ghost and a slot for your artifact, but neither of these are considered armor or weapon and we won't worry about those two.
For the weapons and armor slots you're going to need to have in each one a Legendary or Exotic grade piece of gear. These gear pieces are color identified, Purple for Legendary, and Yellow/Gold for Exotic. Any weapon or armor piece can be acquired through random drops in any activity in the game.
Crucible combat affords a fairly high degree of repeat drops for players, but if you're not into PvP combat, I recommend grinding out the Strike playlists. For a more direct purchase route on pieces, make sure to do weekly activities such as the Story playlist, Vanguard Strikes, and the featured Crucible mode. Each one of these activities will net you Legendary tokens that will allow you to purchase items directly from specific Vendors in the Tower, the Reef, or the Iron Temple. If you want random legendary loot, purchase a box from any of the three Cryptarchs. They have a rotating supply of Legendary drops. For very specific items, go to a Vendor; The New Monarchy, The Future War Cult, Dead Orbit, The Vanguard, Petra Venj, Lord Saladin, or Lord Shaxx. Each one will give you specific items you can purchase.
As for Exotic pieces, your best bet is to find Xur. He appears randomly in different locations around the Tower and the Reef every Friday and Saturday, and has a rotating stock of items that changes each week. He only accepts Strange Coins; and Strange Coins are random rewards for completing different activities throughout the game. Other methods of getting Exotics come from completing Raids and the weekly Nightfall Strike.
For the achievement, you're going to need to do a bit of grinding, and acquire the eight pieces you need. One primary weapon, one secondary weapon, and the heavy weapon; then you have the Helmet, Gauntlets, Chest, Legs, and Class item for the the armor. You can only equip one Exotic weapon and Exotic armor piece at a time, so you can fill two slots with Exotics, but the other six will have to be Legendary level. Once the eight slots are appropriately filled, you're now "Suited for War".