Arachnus-X is vulnerable to both Normal Beam or Missile attacks from the front. (On route to the boss, Samus can acquire two additional Missile Tanks which are helpful.)
There is a ledge on both sides of the room. Begin pummeling Arachnus-X with missiles once the Core-X manifests into that form, and be prepared to quickly dodge incoming flame and energy attacks by jumping back onto the nearest ledge. Arachnus will then attempt to roll into the wall to try and dislodge Samus's grip, so jump over to the other side of the room before he hits the wall. Repeat this process of shooting, dodging, and jumping to the other side of the room until the Arachnus form is defeated. The Core-X will re-appear and can be destroyed through a stage of three single Missile attacks.