To easily defeat all Robot Masters, simply fight the bosses in the following order, collect their weapons, and use those weapons on the next boss on the list.

Acid Man (Weakness: Block)
Impact Man (Weakness: Acid)
Bounce Man (Weakness: Impact)
Fuse Man (Weakness: Bounce)
Tundra Man (Weakness: Fuse)
Torch Man (Weakness: Tundra)
Blast Man (Weakness: Torch)
Block Man (Weakness: Blast)

After defeating the eight Robot Masters, you will unlock the final Fortress stages, and fight Dr. Wily. These bosses have the following unique weaknesses.

Wily's Fortress Stage 1: Use the Buster against the eye.
Wily's Fortress Stage 2: Use Fuse on the exterior, and Impact in the center.
Wily Boss Battle Stage 1: Use fully-charged Blast.
Wily Boss Battle Stage 2: Use Fuse from below.