The Explorer's Key is a use item that you can find by default (doesn't need to be unlocked). Simply collect this item, find a golden chest, and use the key by pressing
. I have only found golden chests on the last and second-to-last levels.
If you want to make this easier, equip the Command Artifact. To unlock this, go to the top right of the map Hive Cluster, and jump across the strings to the artifact. If it isn't there, instead if going to the last level, keep replaying old levels until it appears.