He had arc shields and I used my Despot SA/5 rocket launcher with the tracking perk on him until I was out of rockets. That took his health bar down about 3/4 of the way. I then switched to my fusion rifle and that wasn't doing enough so I loaded a heavy ammo synthesis and attacked with the rocket launcher again. It took a bit of doing but I got him and I was stoked, it was one of the best fights I had. Now, there was a similar Fallen captain with solar shields public event in the mothyards but I was up at the entrance to the Skywatch building up on the little building at the overlook. I saw a lvl 28 try to solo him and shot about 14 rockets from the same launcher at the captain, all of which hit their target. Arc doesn't beat Solar sadly. He got away. I wish I had the targeting perk on all my rocket launchers, I've soloed the Devil Walker in the Divide many times due to that perk on my launcher.