This can easily be done in the first one or two levels. Just play through like normal but make sure you explore every area, find all secret rooms, defeat all enemies, and open every chest. If you're lucky you'll get a piece of armor, but nine times out of ten you'll get gold. If you don't get the three items by finding them off dead enemies or in chests, go to the merchant in the city and buy the cheapest ones for a full set.
You do NOT need a shield for this achievement.
To pick up armor/weapons, walk over them and press when you get the prompt. To equip them, hold down to open up your inventory, then highlight the item you want, then press to equip it.