Core-X that fire beams are more difficult to take down, as they can only be damaged by shooting them in the eye. The eye opens once every three seconds, so make sure you have some distance between yourself and the Core-X - you may want to leap over it once or twice or run from one corner of the room to the other. Once the eye is open, it will wait three seconds before charging and firing a beam shot. During this time, you must shoot it with a Missile or Charge Beam. However, once you shoot, immediately jump in the air, as the Core-X will reflexively counter with a beam shot. Once the Core-X is defeated, it will leave behind a beam powerup.