Unlocking this forge (and the others) is a grind! For the portions of the quest that require killing "powerful enemies" with power weapons, it is recommended to load into the Leviathan raid landing area, kill the initially docile yellow bars w/your power weapon, pull out your map and then reload the Leviathan raid. Rinse & repeat for all the steps that require it. You'll get a single fresh clip of power ammo when you land, so stretch it out with something like the Thunderlord.
Like the video below states, stick to the blue tinted caves on the right to collect batteries to charge the forge. It is a lot safer there with all the cover provided and forces enemies to come in close for combat.
With the boss (level 3), we actually recommend going to the back left area just beyond the crate at the entrance of the cave overlooking the cliffs. This forces the boss to stand in your line of sight while giving your team some cover from all the enemies. A Warlock with a rift and/or Well of Radiance will help make this an easy fight. A Titan rally barricade or Warlock w/Lunafaction boots will help grind the boss with auto rifles/machine guns.