Beast Quest

To open iron chests you need iron keys. Press by the chest and it will open if you have a corresponding key in your inventory.

There are plenty of iton keys and chests along the main quest path. You don't need to backtrack to open every chest. Simply pick up the keys and open chests as you travel through the forest. They appear on the minimap and are usually very easy to find. I had unlocked this achievement within a few hours of gameplay.