Teenage Mutant Ninja Turtles: Shredder's Revenge

Note that, if you're playing in co-op, this achievement requires the entire group to not use a credit throughout the entire Arcade Mode. Bear that in mind, that you can't just focus on yourself; if a teammate or party members has to use a credit, this achievement is voided on that run. This also applies to online lobbies. For example, if you join an online lobby that is already 95% of the way done with the game, if any of those party members has used a credit at all before you joined, you can't get this achievement in that lobby's run of the game.

That being said, joining a session in progress for an online lobby is still a viable method of getting this achievement quickly and easily, it just relies on luck that no one has used a credit by the time you joined, which you'll have no way of knowing. Joining a lobby that is playing on Chill difficulty with at least two people will at least minimize the likelihood that a credit hasn't been used, since Chill is pretty easy and in co-op they could revive each other. With lobbies still existing two years after the release of this game, you can pretty easily monitor and track online games and jump into a Chill lobby toward the end of a run and hope to get this achievement, but it is going to come down to getting lucky that no one used a credit.

Doing this "legit" isn't bad at all with a co-op partner. Solo, it would be very challenging. Getting through the levels themselves isn't bad considering there are typically two or three pizzas along the way to get you to full health. The problem is that you can't heal during boss fights, so you'll need to beat each boss fight without dying to minimize the chances of needing to continue by the end of the game.

In co-op, this is far easier. To put it in perspective, my very first playthrough of this game was with my five year old daughter, neither of us having played this before, and we beat the game without using a credit. We revived each other numerous times throughout the game, and there were deaths, but we each had plenty of lives and plenty of opportunities to revive each other to prevent deaths. We finished with still two lives each at the end of the game. All of the tips in Like the Old Days! (35G) can be applied here for reducing the likelihood of dying. On Chill difficulty, enemies go down really easily. Bosses can be treated the same was as described in that solution to avoid taking too much damage and dying: taunt during downtime to fill your special, wait for them to rest between attacks, do a normal combo, then use a special attack, then retreat and repeat.