In the SNES version, the charge shot carries a unique property in giving the player extra elevation to their jump if properly timed. This is what is utilized to skip the first miniboss of SNES Lawnmower Man.

When initially learning this trick and successfully getting it myself, I looked to the small gap between the trees (with more detailed spritework) in the background. This is indicated with a "white" line.

Using that I found that the beginning of that gap (indicated with a "blue" line right underneath the white line) is when you want press and hold the charge shot button. This of course is assuming you are continually moving right as you do this.

From there the timing of the jump becomes simple. Just jump right before hitting the end of the structure Dr.Angelo is currently standing on in the picture above (which is the stone wall).

If done correctly you should be able to get right to the top of the building where the yellow line is, thus skipping the first miniboss and the roundabout route that follows.

As for learning how to get this setup fast, I start by holding the charge button as I exit out of cyber industrial zone and unleash the first charge shot on the ground level before I jump onto the stone wall. This charge shot will force the monkies(?) to jump onto the stone wall.

After unleashing the first charge shot, I charge up another one right after and unleash the second one after I land on the stone wall. This forces the monkies(?) off the stone wall as you approach the spot specified in the picture above.

Done correctly in real time it should look like the video below.