Teenage Mutant Ninja Turtles: The Cowabunga Collection

The easiest (and cheesiest) way to get this achievement is as follows,

Use the enhancements on the game selection screen to be able to play as the bosses - Triceraton, Krang and Karai

Set level to 8 for your opponent, keep their speed at 4, make the match only for 1 round.

Start the game as Karai and then press start on a second controller, select the same char you was due to fight (if you was fighting Leo then select Leo etc etc) and put their level to 8. Now all you have to do is beat up the second player char who can't move.

Rinse and repeat for all 8 chars and then do the same for Triceraton and Krang (their chars are darkened out silhouettes above the 8 fighters you can normally pick)

The only battle you can't jump in the second player for is Karai.
This is your only actual real fight and it's pretty simple if you abuse the rewind function.

After you beat her, achievement pops and you're done.

Good luck.

G Tournament Champion - 100g

I found a (relatively) foolproof method that worked for me here and saved me a buttload of time. I suck at fighting games, but I played this one a lot as a kid. This method relies heavily on the Rewind system and spamming saves, which is a godsend to make this achievement easier, having played this legit back in the day.

1. Choose Options. You want Level 8, Round 1. This is the highest difficulty (vital for this achievement - the real Karai will not spawn otherwise). It also gives you one round to win, minimising your suffering on your run.
2. Press start (Menu) to exit.
3. Choose 1 Player. Choose April. Pop your power up to 8. Leave the speed alone. (action frampton has reported in feedback below that using Karai is also a good strategy here. If April doesn't work for you, maybe switch to Karai instead. The solution below will pertain to April because this is the method I used).
4. Choose any planet on the Stage Select screen. Doing this sets your path for the game.

April seems like a bizarre choice, right? Well, that's because she has some ultra cheesy moves, which will help you massively. Crouching and pressing A will have her kick in the direction of her foe, sending your opponent back and dealing some damage. Crouching and SPAMMING A will make her slip into a frenzied clawing motion, similar to E-Honda slaps or Chun Li kicks on Street Fighter. Crouching and pushing away from your opponent helps you block.

9 times out of 10, the enemy can NOT jump over/interrupt the claw attack and it also deals huge damage too, while minimising their progress. The kick gives you a safe way of distancing the opponent from you, so they can walk back into you again. Using this method, I completed the whole run in less than 30 minutes. It's best done in the corner so the enemy cannot jump over you mid-spam, but it can work anywhere on the screen if the AI gets a little cocky.

Be ready to adjust for their offense, though. Sometimes they cotton on to your cheesy ways and can wreck you very quickly. Just move away and settle back into the spamming again on a different part of the screen. Don't be afraid to use other moves though, if you see a chance to strike. April also has a decent jump kick that works well if used as she drops down onto the opponent. Some enemies will block aerial assaults though, so it's best to stay grounded if you can.

This is a difficult achievement for a reason, though. You will need to rewind regularly if the opponent figures you out, and SAVE SAVE SAVE at the end of each match. Luckily, you only have one round to survive, which speeds this up. You can save mid-match if you like, but the rewind feature could leave you high and dry, so it's best to redo the entire match to prevent being stuck in perma-death situation.

Like I said, this is relatively fool-proof, with a little patience. Once you rinse all the planets, the achievement is yours. Good luck!

Use Karai she is OP I couldn't even hit anyone on easy until I tried Karai and then just Roman Reigns superman punched everyone in a few minutes.

See the video for a better understanding.

Turn ON Boss Playable characters under enhancements (back/ select button before you open the game)
then set the game to-
Level 8
Rounds 1
Timer ON
Continue 7

Select 1 Player

Select Karai
Speed 8
Power 8

TMNT Tournament Fighters (Genesis)

Before you enter the game press the Squares (Select) for Enhancements. Turn on Playable Bosses.

Start the game

Go to Options → Change Level to 8, Round 1

Go to 1 Player, choose Power 8 Speed 8

When the game starts press Start on a second controller.

Choose the Character you were fighting and beat the helpless opponent, Press Start when it goes to replay

Repeat for the remaining fights

When I reached Karai I had to fight legitimately. Abuse the Rewind LB.

You have to play on max difficulty. I recommend 1 round matches as well as using rewind a lot. Now characters like Casey and Karai have a notably longer grapple range. You can quickly trap your opponents within doing throws or constantly beating on them moves. Here I quickly played through the entire game as Karai.

You have to finish it on the highest difficulty.
Set it to 1 Round and rewind a lot during and save a lot after the fights.
I picked April because her crouched Kick has proven very effective in a lot of fights.