The B.O.X. is fought two times.
PART 1: When it appears in Sector 3, immediately run to the left, jump and cling to the ceiling and allow it to run past you. Depending on which side of it you are on, it will bend down and launch a thermal grenade, which creates a large moving pillar of flame when it detonates. Make sure you are far enough away from it so the trajectory of the grenade will not touch you. Right after avoiding the grenade, move so you are directly above its central body. Aim directly down, fire a single Missile, and then keep moving in the same direction. It will then try to throw another grenade at you from that side. Repeat this back-and-forth process until it decides to run away.
PART 2: When you encounter it, immediately drop a Power Bomb to reveal the grips on the ceiling, and jump to cling on to them. Fortunately, B.O.X.’s attack pattern hasn't changed much, but it is also electrically charging the water below, so don't jump in! Move far enough away from B.O.X., and it will launch its homing missiles at you. These homing missiles can be a pain, but they are easily destroyed with your normal beam, so just keep shooting them until they are gone. Then move back above its center, aim down, shoot a missile, and keep moving forward. Repeat until it explodes and reveals a Core-X. Go to this entry for more information on fighting it. After its defeat you will receive the Wave Beam.