Eggman's plan. He travelled to Lost Hex, knowing what he would find, met Zavok and the rest of the Six, somehow overpowered them (either by use of the Cacophonic Conch or sheer force of numbers and superior technology) and managed to beat them into submission. Keep in mind these guys are incredibly powerful and all seem to have strange powers. If it weren't for Sonic screwing everything up by kicking away the Conch, Eggman could very easily have won this time around. Even when he does get betrayed, he thought everything through and did everything right this time around - he just happened to overlook that headstrong hedgehog that followed him there.
Eggman's backup plan is even more brilliant. After Sonic kicks away the horn he was using to control the Zeti, Eggman is left without his army, boss mechs, or even his Egg Mobile. With nothing but his own brilliant intellect, he teams up with Sonic, depending on him to defeat the Zeti so that he can fake his own death and utilize the planet's stolen energy to power a huge, world-conquering mech (without the threat of the Zeti's machine-controlling, since Sonic took care of them). After losing control of his entire plan, Eggman clawed his way back to the final boss position with nothing but his own cleverness.
At Frozen Factory, Zavok and Zazz contact Sonic, Tails, and Dr. Eggman through a transmission on a screen of ice. As Zavok and Zazz boast on how they're gonna sap the energy out of the world along with everyone on it, Eggman suddenly loses it and completely destroys the ice screen with his bare hands. He doesn't even suffer any injury, as he says that his hands are fine, as long as he can strangle a Zeti. Even Sonic and Tails were surprised by his burst of rage.
Actually, he does hurt his hands. He simply doesn't care.
Zazz: Where are you gonna live when your world's dead, guys? Oh, right! YOU'LL BE DEAD, TOO! (laughs maniacally) Too bad for you! (continues giggling)
Eggman: I will burn your worlds, you rebellious scum. I will destroy everything you love, and make you watch! (punches the screen repeatedly) I'll... I'll...I'll...! (with one last hit, he shatters the screen completely)
Orbot: Boss, your hands...!
Eggman: As long as I can still strangle a Zeti, my hands are fine.
Tails' epic comeback in Lava Mountain. He reprograms the computer that's supposed to make him a robot slave so he can keep his free will. Then he plays along until the Zeti asks him to destroy Sonic, upon which he proceeds to shoot the Zeti with the arm cannon they gave him, giving Sonic enough time to chase after them. Then he reprograms Eggman's machine that sucked all the energy from the planet to give it all back, saving the world. Nice to know Sega hasn't completely forgotten his Badass Bookworm status.
Tails: In your face, Eggman!
Sky Road Zone 4. After all the nonsense Zavok has put Sonic through, Sonic goes after him, dodging giant robot dragons and climbing through the sky just to reach the Zeti. Then there's the boss fight that wraps up the level. Zavok and Sonic duel on top of Zavok's massive dragon mech while a storm rages in the sky and epic orchestral music plays. And how do you beat the fight? YOU SEND ZAVOK FLYING OVER THE EDGE OF HIS MECH WITH A FULL-POWER HOMING ATTACK AFTER KICKING HIM IN THE FACE.
An out of story mode example. Two DLC levels based on Nintendo games were added into Lost World, one of them being based on Yoshi's Island and the other based on The Legend of Zelda. The sheer amount of detail and fanservice loaded into these stages, particularly the latter, is RIDICULOUS.
Sonic's Tranquil Fury moment towards Zor after Tails is captured, marching up to the confused Zeti with a fixated Death Glare and very firmly telling him he wants his friend back. Now. Without even raising his voice or a fist, you can tell they've really pissed Sonic off.
Even the final Zavok battle is filled with awesome. It seems like a normal battle, and you finally beat him. Until he pulls a full-on Giant Bowser and emerges as a giant. With the use of floating platforms, you must advance to the top where a final switch is pushed, sending the colossus to his fiery grave.
Even after he lost everything, Eggman promised the Zeti their inevitable destruction, punched down a wall of ice without breaking his hand, and threw in a Badass Boast about strangling Zeti for good measure. THIS is why he's the Big Bad, ladies and gentlemen. THIS is why he's Sonic's Arch-Nemesis.