Bull's-Eye Banzai

Bull's-Eye Banzais, originally known as King Bills, are the red heat-seeking variants of Banzai Bills and a larger variety of Bull's-Eye Bills. They attack by homing in on the player.

New Super Mario Bros. Wii
King Bill only appear in World 9-3 of New Super Mario Bros. Wii. Unlike Bull's-Eye Bill, they only have a limited homing ability where they will track their target's vertical position and then continue forward once they reach that height. Their animation is very limited as well, always maintaining a horizontal position and never turning to point at their target.

The player can defeat it by simply jumping on its head, or by running into it with a Super Star. Also, a King Bill cannot be frozen by an ice ball; it will break the ice and release itself when the ice ball reaches it. Likewise, POW Blocks are useless against them.

King Bills are never seen being fired from a Banzai Bill Cannon.

Super Mario 3D World
Although no actual King Bills show up in Super Mario 3D World, another Banzai Bill variant, the Cat Banzai Bill, behaves similarly.

Super Mario Maker 2
Bull's-Eye Banzais appear under their current name in Super Mario Maker 2. Unlike previously, they can move on every angle, like the Bull's-Eye Bill, and the marks on their eyes are red, like the normal Banzai Bill, instead of black. In a vein similar to Banzai Bills, Bull's-Eye Banzais also receive new designs for all of the present game styles, barring New Super Mario Bros. U, in which their designs are mostly retained from New Super Mario Bros. Wii, albeit in high-definition and with the new marks around their eyes.

Trivia

 * The King Bill is one of the two new enemies from New Super Mario Bros. Wii that do not return in New Super Mario Bros. U, the other being the Obake Stand.