Ramming kill!
After shooting it a little, the status bar looked like both the shield and the hull were empty. So I presume it was the cusp of death. That's when I kicked the in the afterburner and ran into the Bloodhound. And it actually killed it! (And ended the mission, etc).
I didn't think that ramming caused much damage, but I guess it does cause, like, 2 points of damage or something
ER