Got it! While he's in the shield he regenerates. The trick is to get him out of that shield ASAP.
For those interested here's what I did:
Using the Pacifican machine gun I shot the green spots on the big bad until the shield came up. Once the spires came up I used the Black Widow to bring them down with one shot. It takes quite a bit of practice to be able to avoid the diggers and do this, but it can be done.
I get him down to the point where he has his shield up, the spires come up, and he brings in a ton of those diggers. In fact I got him to this point 5 times in one round. But each time he comes out of that shield he's all healed up.