The reactor is the Halberd's main power plant. It is a large room where Wheelies continuously run within chambers to generate power, but the part of it that is fought looks like the central conduit of some sort, with a floating crystal shaped like an square bipyramid.
In Kirby Super Star and Kirby Super Star Ultra, the reactor is guarded by a set of auto-defenses, including a pinpoint laser gun on an extendable arm, a large pulse cannon, and a series of burners under the floor. According to Sailor Waddle Dee, the reactor is invincible unless it shoots itself (via the laser gun), making its defenses its own weakness. Since the laser aims at Kirby/Meta Knight, flying next to the reactor's crystal and then quickly getting out of the way of the crystal is an easy way to defeat it.
While all of the auto-defenses can be destroyed, it is often impractical to do so, as only destroying the core is necessary to win. The pulse cannon has high enough health that there would already have been enough laser beams fired to destroy the reactor by the time Kirby gets rid of it, unless Kirby is wielding a powerful ability that can destroy it within three cycles. Meanwhile, the burners can only be destroyed by attacks that reach below the ground. The burners and laser gun will eventually regenerate, though the pulse cannon will not.
Kirby encounters the reactor in yarn form in Kirby's Epic Yarn and Kirby's Extra Epic Yarn while traveling through the Halberd on the Star Shooter. Unlike in Kirby Super Star (Ultra), it can be damaged normally, and Kirby (or Prince Fluff) must destroy it by firing on the central crystal. The laser is replaced with UFOs that attack with their Smart Beams, and the floor burners and cannon are replaced by two flamethrowers, one at the top and one at the bottom of the reactor. These are also capable of blocking the Star Shooter's projectiles.
Wheelies are not seen in the background of the reactor in this game, possibly suggesting that the Halberd is using a different energy source.