In order to destroy a Watcher Knight, you must hit if with a lot of firepower using any weapon. Once it starts to catch on fire (blue fire, that is), you have almost beaten it; it should go down after only a few more shots once it is this injured. Alternatively, for a quick kill, it is possible to move in close with the jet pack for a QTE.
If you get too close to a Watcher Knight, it will grip you with its tail and try to make some holes in you with its minigun. unless you get free.
Knights mostly act as mini-bosses in Dark Void, as they are fairly easy to take down, yet much harder to kill than, say, a Silver Watcher Pawn. However, it is imperative that you stay in cover to kill a Knight, due to the fact that it can tear you to shreds with its miniguns if you stay out in the open for too long.