For beating all the bosses, here are all their weaknesses.
Possible Spoilers. If you want to try to learn their weaknesses yourself, then don't read.
Here is how I did it, but you can start with whoever you want. This was just the easiest way for me.
Pump Man ? Solar Man ? Chill Man ? Nitro Man ? Commando Man ? Blade Man ? Strike Man ? Sheep Man
Dr. Wily Castle 1:
Capsule Machine Part I: Elect Man - Wheel Cutter, Gemini Man - Wheel Cutter, Wood Man - Triple Blade
Capsule Machine Part II: Ring Man - Solar Blaze, Napalm Man - Ricochet Shot, Flame Man - Water Shield
Capsule Machine Part III: Slash Man - Chill Spike, Tornado Man - Thunder Wool, Frost Man - Commando Bomb
Dr. Wily Castle 2:
Crab Puncher - Commando Bomb or Thunder Wool
Dr. Wily Castle 3:
Block Devil - Ricochet Shot
Dr. Wily Castle 4:
Dr. Wily Form 1 - Solar Blaze
Dr. Wily Form 2 - Water Shield
Dr. Wily Castle 5:
Wily Capsule - Chill Spike
And that's all she wrote. Hope this guide helps some of you.