Mighty No. 9

You need to start a new save file for this to work.
I used the following strategy:

Brand (Mighty no 7)
Electric lady (Mighty no 3)
Shade (Mighty no 8)
Avi (Mighty no 6)
Pyro (Mighty no 1)
Cyro (Mighty no 2)
Battalion (Mighty no 5)
Seismic (Mighty no 4)
Then the remaining levels in order.

Here is Calebhart running the game in 56 minutes game time.
https://www.twitch.tv/calebhart42/v/73957190

You want to go fast and avoid as many battles as possible but you can slow down to get a life tank if need be remember it is better to go slow then to die.

I ran through the entire game and died once on Mighty no 3. Finishing with 51 min 5 sec.

Practice each level to learn the patterns and levels. By using the above strategy you are able to use the boss weaknesses making the fights fairly easy and quick.