Double Punch

It seems to be possible to get two punches in a short time period, including against bosses. This would be a massive timesaver. However, it is currently not understood.

Example:

Penguin Movement Manip

If you jump at penguin from the left and punch, you'll force him back to the left. Not sure if this saves time.

Example:

Cat Woman Skip You can avoid the 2nd Cat Woman fight by jumping over her loading zone. This is seen in the world record video.

Sticky Robin

If Robin punches at the same time he grabs a ceiling, he'll get frozen in place. If an enemy bumps you, you can get out. I don't know any other way to get out, but I have seen someone break free without an enemy collision in a casual playthrough. No idea how they did it.

Behind the Background

You can go behind the background in stage 1. This is not currently understood.

Example: