This demo, recorded on ACE difficulty, shows how I defeated the level 4 boss. Basically, I snipe at him from the outer ring, sliding to avoid his return fire. It might not be the fastest way to do him in, but it is effective and relatively safe.

As the demo starts, I am positioned outside the fence-door entrance to the boss's lair. Just to the left of this door is a switch that unlocks all the other doors to the central room. I trigger this so that I can employ my sniping technique.

I then grab the hidden cloak near the hostages and proceed to release the boss from his "cage." I feed him a Mega and quickly exit to the outer ring. (Had more time on my cloak than I thought. I definitely could've fed him some more ordnance here.)

All that's left now is to snipe, dodge, and repeat until the exit door opens. :-) I would like to call your attention to an important tactic, though. When the diamond-clawed lifters chase me into the outer ring, I switch to the Gauss cannon to take them out, since they don't release the homing green balls when hit with matter weaponry.