Wasn't the Destroyer unable to fly? If not, the thing gets chucked into space.
Also think about the offensive feats for the Destroyer for a second. Its beam killed featless frost giants, correct? Then it was messing up a small town and blowing up cars and stuff. I don't recall any power output on the level of doing significant harm to Supergirl. The most you could say is Thor blocked the energy blasts with his hammer, but that isn't an offensive feat for the Destroyer.
It has been a long time since I saw the first Thor movie though.
Also since Loki survived the Shield gun it's not really going to do much to Supergirl. The regular Shield agents might as well not even be there.
It sounds like this is going to turn out to be Supergirl tries to do damage to the Destroyer, if she figures out she can't she could just space toss it. Then just slap down the Shield agents.