The Gotchas only appear in Speed Slider. In gameplay, when the players reach a certain position in the level, they will come in from beyond the screen (that is, they show up as large as possible, shrinking as they approach the game field) and home in on the nearest playable character. If they grab the character, they will be surrounded in a ball that will suck away their rings one per second. When this happens, make no attempt to destroy them except with the other playable character, as they will follow the captured character's movements.
Like many of the Badniks in the game, Gotchas are powered by synthesized Rings which they drop upon defeat.