Sonic the Hedgehog 4: Episode I

The Egg Carrier zone is pretty much a trial-based recap of all the bosses you've played so far, as well as an updated version of the final boss in the Death Egg zone in Sonic 2. The first 4 are cake, as you already know what to expect.

This is not the case for the final boss. It took me roughly over 30 tries to beat him.
Once you deal a certain amount of damage, he starts to go into a "hyper mode" in which he's enveloped in an electric field and you cannot touch him. He'll run back and forth across the screen frantically trying to smash you. You can't jump over him. Instead, time your steps and run or spin dash underneath him. When he shoots his arm out, it'll fall to the floor. Hit it 3 times to send it back and stun him, at which point you can start wailing on him. Rinse and repeat. Eventually he falls to the floor, which collapses, and you die. So instead of dying, run for your life.

IGN posted a very generous guide in which I am in no way associated with, Thanks guys.

NOTE: if you intend on getting the Sonic mask avatar award, take note of the ring pattern at the end!!!

The final level is just a boss-rush style scenario. Fight all of the bosses (most of which only take four hits to kill) followed by the final boss. The final boss is similar to Sonic 2's Death Egg boss. Learning the patterns of the bosses will make this simple.

You do NOT need all of the Chaos Emeralds to get this achievement. Just clear the final level, watch the credits, and once the post-credits ending rolls, you'll get the achievement.