Robotnik's Evil Plan involving the Drakon Empire, resulting in him absorbing the power of the Chaos Emeralds, ruling over Mobius for eternity, and being capable of tormenting Sonic in any way he could think of.
Sonic's defeat of Robotnik here counts too, as it's one of the few times that he used his brain to defeat Robotnik, simply by appealing to his vanity and new found god-hood by pointing out that if Robotnik was so powerful, it wouldn't matter if Sonic had an ally or not, Robotnik would still win. Robotnik buys into it, and lets Sonic choose one person - Sonic chooses Knuckles, the Guardian of the Chaos Emeralds, who promptly uses the Grey Chaos Emerald (The "control" emerald) to defeat Robotnik.
The reason they defeated Robotnik to liberate Mobius counts here too, as the Omni-Viewer states that Super Sonic will cause a planet-wide EMP when he explodes the asteroid he was trapped in. Sonic immediately asks the Omni-Viewer if he can move the asteroid above Mobius, and when asked why, he simply smirks and says "Because most of the technology on Mobius is Dr Robotnik's!"
Robotnik doing the one thing Sonic couldn't do: defeat Commander Brutus.
Knuckles destroying Carnival Night Zone with by punching a fault line near the Zone with one punch. Since the Carnival Night Zone was built on the edge of the Zone, Knuckles completely smashed off that portion of the Floating Island, removing Carnival Night from the island. A few seconds later, the Zone fell to Mobius, slightly cushioned by remaining Master Emerald power. The crash-landing of the ruined Zone was a shock to one Emerald Hill boy who had just before wished that the Zone was closer.
Knuckles helping Sonic to stop the Death Egg II by using the Floating Island and the remaining six Chaos Emeralds (Robotnik has the Green Chaos Emerald which is the Master Emerald) to power the ancient technologies installed throughout the island. With the island effectively turned into a flying fortress itself, Knuckles steered his home toward the Death Egg, unleashing a barrage of energy blasts that tore through the vessel's armored hull, destroying the Death Egg II.