This achievement is earned by finding or purchasing weapons and armour. If you find any duplicates they will only count as one. This shouldn't be too much of a problem if you are carefully searching each area you enter, buying every weapon and piece of armour at each vendor you find, and completing all the pre-planned quests and lots of notice board quests. This will probably be obtained during your second playthrough. You should have lots of gold during it to buy all the equipment you find. If you fight the Ur-Dragon you can also get weapon and armour drops from defeating it. You can receive different equipment each time you defeat it.
Check your progress with this achievement in the Adventure Log. It will unlock once you have collected 350 different pieces across all playthroughs.
There is also DLC that can be purchased to count towards this.