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Warning!: You cannot let time run out, so when it comes to I-No you cannot use the keep away method, it is best to set your time to infinity so this isn't a wasted run.
Anyways, you fight through 10 stages, the first 9 stages are easy enough. You can use Instant Kills which will take a lot of the difficulty away. To do an Instant Kill you have to input this (its the same input for most characters, Dizzy and May have different ones though).
P + K + S + HS > 236236HS
This can be done as soon as possible. I recommend using Justice, to unlock Justice, you must complete her Story Mode.
Then when it comes to the I-No fight, its easy enough, but you cannot use Instant Kills, her worst attacks are the ones she does at certain points of her health, you can get lucky with these where she does the easily avoid one. There is three types, one where she covers the screen, it is best just to block here. One where there is a opening in the middle, when it starts you have to start walking slowly towards her. I found it easier just to block this one too but if she does three of these on you, its impossible to win that way. Then there is the easiest to dodge one which at the far side there is a opening, just go there and crouch and it shouldn't hit you at all.
Very rarely, she'll change the pattern before she unleashes the move so be prepared to move just in case.
You can change characters during this and the achievement should still unlock, you can use as many continues as you want.