Teenage Mutant Ninja Turtles: Shredder's Revenge

As the description says, you need to defeat Super Shredder, the final boss of the game, without being hit. A couple points to clarify:
 

• You can get hit by Krang in the fight preceding this without impacting this achievement (even though the ingame challenge for beating the episode without taking damage will fail)
• This requirement applies to everyone in the group in you're playing co-op, not just yourself. In other words, if anyone gets hit, this achievement won't unlock for anyone in that group

That being said, there are two ways to unlock this achievement: the easy boosted way, or the very hard legit way.

Easy/Boosted Way
The easiest way to do this is to first beast Episode 16 yourself so you can play it online, and then find a boosting partner online (can't be local). The boosting partner will play Episode 16, beat Krang, then fight Super Shredder. As soon as they land the killing blow on Super Shredder, pause the game. Press  to enter Party menu, choose to Create A Party, and then invite the person going for the achievement. As soon as that person joins the game, the pause will end (since it's now an online game, so it can't be paused). The person who joined will unlock this achievement immediately. Now simply repeat this process with the roles reversed so the other person can get the achievement in the same way.

Note that, if you don't have a boosting partner, you can still attempt to get lucky by joining an online game. You can scope out the online games and join one in progress in hopes of getting this. One way is to go to Story Mode, after beating Episode 16 highlight it, then press  and it'll search for lobbies on that specific episode. You can then try to join one at the end of the fight and get lucky to unlock this achievement. However, in my experience, I virtually never found lobbies in Story Mode at all. The other option is to track lobbies in Arcade Mode. This mode spans the entire game and isn't just the final fight, obviously, but you can adjust accordingly. Track the completion percentage of each lobby to see where they are. The game hits 95% completion at the start of the Super Shredder fight and stays there until he's defeated. So, continually refresh with  until you find a game at 95% completion (or one you've been watching gets that far), and then you have to try to time your joining to get it right.

IMPORTANT NOTE: The joining of an online session to get lucky ties into the second bullet above, where if someone gets hit, no one gets this achievement. How this works for this method is that, as soon as you load into an online lobby, that's when this achievement starts looking for the fail conditions for all party members. What this means is that, from the time you join the lobby until Super Shredder is defeated, NO ONE can get hit, not just you. This is where the luckiness of the timing comes in, because if you join a lobby at 95% and they're still in the middle of the fight, if they take damage you won't get the achievement. This is why the boosting method above works perfectly: you're joining at a point where it's impossible for the host to take damage. Without a boosting partner, you need to join and hope no damage is taken. Or, if they get hit, you can leave the lobby, wait until you think they've beaten Shredder, and rejoin with the hopes that it's further into the fight and no damage gets taken. This is a complete toss of the dice though, as you can tell from the description. Better to just find a boosting partner and you can do this in five minutes.

Legit/Hard Way
Doing this legit is quite challenging. Definitely attempt it alone if you want to do it legit, because you definitely don't want to have to rely on others also not getting hit.

Super Shredder has three main attacks:
 

• Teleport/dash at you to try to grab you
• Dash around the area leaving a fire trail
• Shoot out waves of fireballs on the ground

All three of these attacks are a pain. The first is impossible to predict. I try to roll, but if he decides to dash in the same direction as your roll, he'll still grab you. Best to double jump up or down on screen to avoid this, since he only seems to dash left or right, not up or down. For the second attack, I tend to stay in one of the corners and only move if he's coming in my direction. He seems to go to the corners pretty rarely. For the final attack, it is possible to get between the fireballs so they can't hit you, but it's way safer to just jump over them quickly. He'll finally do his little burst of energy and then be vulnerable to attack. You're basically repeating this over and over throughout the fight, trying not to make a mistake and get hit by one of his dashes or fireballs. Eventually, he'll spawn four purple statues to destroy. These are far easier. You can typically get two on the same side before they start shooting, and then roll across the screen to get the others.

This is still a pain and very challenging though. It'll take a ton of tries, and it's made more frustrating by needing to beat Krang at the start each time before you even get an attempt at Super Shredder. My experience is that practice is about 60-70% of this, and the rest comes down to luck with how he decides to teleport and dash.