Dragon's Dogma: Dark Arisen

For this achievement, you do not need to have all 350 pieces on hand at the same time. However, keeping them in your storage at the Inn will help you to not purchase the same thing multiple times. I'd also suggest not worrying about this until after you've done almost every other achievement. You'll get a lot of money and unique equipment from defeating the various bosses and selling their materials, as well as doing Bitterblack Isle. You'll likely only get about 100-150 pieces of gear playing normally (just be sure to loot everything you can find!), so you'll need to empty out some stores for the rest.

With a few million gold on hand, head to any of the game's stores. The best one would be Caxton in Grand Soren (especially if you give him the Gold Idol, which expands his inventory). Purchase one of everything with "0(0)" listed in one section (such as weapons). This means you do not have any in your possession (the first number being items you're holding, and the one in parentheses being your storage), and the item will count toward your 350. Now sell them all back and do the same for the next item (such as helmets). Rinse and repeat until you've possessed every item he sells at least once. If that doesn't get you to 350, head to the next shop you can find.

Other shops to try would be Madeleine and Mountebank (both in Gran Soren), Astella (Cassardis), and Alon (Ancient Quarry). This should be more than enough to hit 350 in total.