Titanic Monarch is the final zone for all characters with the exception of Sonic, who can unlock the true final zone by collecting all seven Chaos Emeralds. For the final zone-specific achievement/trophy, you'll have to clear the first act without taking a single hit. This includes getting hit after having obtained a Shield, even if you don't lose any rings. This is easiest to do in Super form, as this makes it impossible to take damage, but if this isn't an option (or if you'd simply rather take another approach due to the ticking down of the rings when in Super form), then either play Tails yourself or have a co-op partner play him. Playing Tails yourself will allow you to fly around and avoid hazards, while a partner can have Tails scout ahead for enemies and clear the path for Sonic (as well as take care of the boss himself). Ultimately, this achievement sound more difficult than it actually is, so the choice is yours, and just remember, practice makes perfect.
Act 1[edit]
Start the act with a Spin Dash to avoid the target of the Sentry Bug and roll into a Super Ring Item Box, which happens to have a spring placed beneath it. Bouncing on the spring will lead you up to a Shield. After dropping back down, you should eventually come across a plasma orb. Jumping onto it will cause you to latch onto and orbit around it. You can change the direction in which you orbit before jumping off, so try to aim upward to launch yourself onto higher ground. After proceeding higher, watch for the poles that summon waves of electricity between them, as well as a Turbo Turtle that will attempt to blow you into them. Time your jumps to avoid these hazards and proceed up a lift and into some bumpers. Use a spring that rises out of the ground only after you've passed it to proceed even higher, where you can find an Extra Life and a spring that launches you toward the first Star Post. Continue to the right.
When you reach a wobbly platform, stand on the left side for a bit; your weight will push the right side up. Once it's high enough, climb it and jump off before it falls apart. Use the bumpers along the walls to climb up, then hop into a kart to be taken to a new area. Continue forward from here, then use some plasma orbs and bumpers to ascend to the left. Past a Ball Hog is the second Star Post.
Proceed to the right and when you come to a stop, pick up the Shield (if needed) and take the higher path. A Turbo Turtle, poles that summon electricity, and plenty of Ball Hogs can be found along this path, so stay cautious. When you've ascended high enough, use some bumpers to reach more plasma orbs, which you can take to the right and up into some more bumpers. You'll have to avoid spikes and electricity when getting through the next set of plasma orbs, so make sure to time your jumps well. At the end of the path, you should find the third Star Post. A platform that slowly rises and falls may make avoiding the spikes a little tricky, but just wait for the ground to reach its lowest point to give yourself enough space to jump over them. Another Shield can be found at the end of the path, as well as a lift that will take you to some smaller lifts. Avoid the spikes on the ceiling on your way to the platform, and follow the path to the fourth Star Post. Stand to the left of the first wobbly platform and to the right of the second to walk off onto the path to come upon an Extra Life. A long climb leads to the fifth Star Post and the act's boss.
If you've been holding off on your Super form, now's the time to use it. The Crimson Eye is what you should be hitting, but the orbs floating around it make this difficult. Once the orbs are out of the way and you're able to get a hit in, one of them will explode, sending spikes in all directions. Dodge and prepare for the next hit. After eight hits, the Crimson Eye will detach itself from the pillar, floating around the screen. The floor that you're standing on will also either rise or fall, making the jump toward it more difficult. Nevertheless, do your best to get some hits in before it attaches itself to the floor or ceiling, as it will then shoot projectiles that bounce off the floor and ceiling; these are easy to dodge if you're prepared. Get eight more hits in while it is in this state to defeat it for good.
Act 2[edit]
Follow the only path forward toward some plasma orbs. If you get a high enough launch off the middle orb (by orbiting around it a few times), you should be able to reach a Shield on the ceiling. Otherwise, use these orbs to head to the right, onto some gears. Across these gears is another plasma orb; if you launch yourself into the purple mist from here, you'll find yourself in the act's hub. There are four paths from here (upper left, upper right, lower left, and lower right). Choose any path to be taken to a new area that you must run through. At the end of that path will be another plasma orb that can launch you into purple mist; enter it to be transported back to the hub, with the cleared area now blocked off. As long as you find a plasma orb and purple mist at the end of every path, the portal leading to the final boss will appear in the center of the hub. Enter it to face Dr. Eggman one last time.
This time, Eggman will be swinging around in his Phantom Egg, which is surrounded by a shield that can't be broken through even in Super form. Eventually, he'll pause to attack. Keep your distance unless in Super form or in possession of a Lightning Shield, as he will take his shield down at the same time he electrifies his appendages, making it dangerous to approach him. Fortunately, there's a small window of time that you can take advantage of, after he concludes his electrocution attempt but before he's able to put his shield up. Get a few hits in and continue the pattern, dodging the rockets between attacks. After sixteen hits, the Phantom Egg will be destroyed, but if you've collected all seven Chaos Emeralds and are playing as Sonic, the Heavy King ensures the fight isn't over.