So I've noticed on many websites on the internet that many players are having problems with this achievement. Collecting 350 unique kinds of weapons and armour can be quite complicated, but there is a way around this.
Firstly, don't even worry about this achievement until new game plus. You'll be wanting to finish the majority of the other achievements in this game before even doing this. Save your second play through for Misc achievements and the long haul ones like Well Equipped and Coin Collector.
Second, try not to sell armour or weapons during dragon's dogma. I'll be explaining why in a few lines. Basically, if your have any duplicates, they do not count as part of the 350, so go ahead and sell those. I would highly recommend getting the exploration achievements out of the way during your first play through so you don't have to go explore and actually find these weapons. Also, make sure you do the hero achievement as well so you'll have access to most of the inventory our wonderful merchants have to offer.
So during new game plus, you'll be able to basically speedrun through this game. During which, you'll hit Everfall and I would suggest killing the Ur-Dragon two to three times during this so you get a lot of wakestones. 20x per kill, which means a good 40 to 60 should be enough. Change your vocation to Sorcerer and grab the rank 2 augment Suasion for you and your pawn. Next, hire two pawns that have the augment as well. They give you 15% extra cash when selling items, and they stack. That 60% is quite nice to have when going for the 10 million gold. Go to Claxton in Gran Soren and sell your wakestones and materials that you've gathered. Your armour and weapons should already be dragon forged by now so you probably wont be needing to find new ones.
I was able to go from 3 million to 10 million this way in one swoop, allowing me all of the cash I need for the mass purchasing of weapons and armour. The reason why I was stressing not to sell your weapons and armour is because when purchasing these items, you'll be able to see how many you actually have in your storage! It'll say something like this. 0 (1). Basically, this means, you have zero in your inventory, but one in your storage. Only purchase items that say 0 (0) and you'll be golden. I had to go by Cassardis and buy everything from her, as well as the merchant by the Shadowfort Rest Camp. Upon doing this, I needed about 90 pieces left, which Claxton has them all, provided you gave him at least a silver idol in your first play through. If needed, you could go ahead and save Madeline again and Reynard and buy from them too. I just didn't really need to, and I skipped most of the equipment that was 100k or more because I thought I didn't have enough money. In the instance where you've run out of money, you can always go farm Everfall for materials and wakestones to sell back. Just make sure all four party members have Suasion on.
Now if you really need to go find some extra stuff, you can go to Bitterblack Isle or keep farming Everfall chests. A bit of advice for farming chests in Everfall, clear the room of mobs, carry Godsbane sword, save, kill yourself, and keep looting the chests over and over again. Eventually you'll find weapons or armour, but I think it's a bit of a time waster. I think farming for Ur-Dragon is much more profitable because Claxton's inventory is like 250 items.