From Sonic Retro
The Egg Dragoon is Eggman's final machine in Sonic Unleashed. This is also the 1st machine shown in the opening, but now heavily upgraded. This is the only battle where you fight Eggman with the Werehog. The goal is to knock its health down to zero.
This machine has 4 attacks: Using a lightning swipe to electrocute you, an Ice Bomb to freeze you, a drill to destroy your fighting area, and unleashing enemies at you.
His weak point is the glowing spheres at the bottom of his machine. You can attack this in a couple ways, including punching it and throwing Eggman's enemies into it.
This fight has 3 stages. Once you get Eggman's health to a 3rd of the way down, his machine will malfunction. You then do a series of QTE's (Quick-Time Events) to destroy some of his machine parts. He will then drill the platform and attack you until you land on the next platform. Each platform is smaller than the last, so beating him quickly is important.
Repeat this step again twice. On the final QTE, Sonic the Werehog will grab Eggman's Eggmobile and throw it into the abyss. This sets the stage for Dark Gaia to knock Eggman away and reveal itself as the true villain.
Take Notice: the QTE's of this boss fight happen only in the PS3/360 version of the game. The Wii/PS2 version removes them, but adds the ability to actually attack Eggman before he has a chance to launch an attack against you (effectively keeping him from ever attacking you (outside of the ground-breaking move he does at 2/3 & 1/3 health)).