Mega Man 3's password system may look pretty complicated, but it's actually pretty easy to figure out. For example, it uses the placement of a single red dot to record how many Energy Tanks you have, and you can totally use this to your advantage.
For example, take this code that I got for having beaten no Robot Masters and having no Energy Tanks.
Consulting the chart below, I know that a single red dot in square C5 means 0 Energy Tanks. From there, it's a simple matter of moving that dot up to A6
To start the game with 9 Energy Tanks, the maximum!
From there, it's a simple matter of recording your password, moving the dot, and continuing on each time you need a refill!
And here's the list of dots and their Energy Tank attributes
# Dot Position 0 C5 1 E6 2 E4 3 B4 4 A5 5 C1 6 D2 7 C3 8 F2 9 A6