Metal Man first, and use Metal Blade against everything unless otherwise it tinks off, or it's one of these robot masters:

Time Stopper (Flash Man) against Quick Man
Quick Boomerang (Quick Man) against Bubble Man
Bubble Lead (Bubble Man) against Heat Man
Atomic Fire (Heat Man) against Wood Man
Leaf Shield (Wood Man) against Air Man
Air Shooter (Air Man) against Crash Man

Honestly, half the bosses are weak to Metal Blade anyways.
This is the only Classic MM game I know of where one weapon is strong against multiple of the 8 bosses.

Flash Man is weak to the Buster as well, meaning he's often a good start point.

Metal Man is also weak to the Buster, and is another good starting point. His weapon makes the game insanely easy.

Quick Man, if you still have Time Stopper, bear in mind a full charge only does half his HP in damage, so you might want to soften him up first. Once he's around half health, use Time Stopper, and take a drink to celebrate your impending victory.

Bubble Man I think is also fairly weak to the Buster. Apart from that, Metal Blade also chews him up quick.

Heat Man, Bubble Lead is the go-to for him, he's pretty resistant to most weapons, and even heals from the Crash Bomber.
(Also, did not know until a month ago, that it's actually "Lead", as in guidance. All these years, I thought it was metal bubbles. But the director of the game clarified it in recent years)

Wood Man, one fully charged Atomic Fire kills him. Otherwise, Metal Blade takes him down quick.

Air Man is weak to Leaf Shield, and goes down to it quick... if you can actually get close enough to hit him, as his tornadoes will block the Leaf Shield.

And Crash Man goes down to the Air Shooter in just a couple hits.