Unusual for when it was released, "Mega Man 2" allowed players to complete the stages in any order. Each stage culminated in a boss fight. Mega Man received the weapon used by the boss after defeating him. Each boss was more vulnerable to a specific special weapon. Boss fights could be made significantly easier by having the correct weapon before starting his stage.
Metal Man is a robot that throws metal saw blades. He has the most unusual weakness of the eight bosses. His weakness is to the Metal Blade, his own weapon. You cannot get the Metal Blade until after defeating him. He cannot take much damage and is not a particularly difficult boss, so the default Arm Cannon works effectively against him. The second time you fight him, you can use the Metal Blade against him. He can take only two hits before dying.
Flash Man's special weapon is the Time Stopper. He freezes time before firing at Mega Man with his own Arm Cannon. Time unfreezes once Mega Man takes a hit. Flash Man's weakness is the Metal Blade won from Metal Man. Flash Man does not have a significant amount of health, so the Arm Cannon is also a viable weapon against him.
Quick Man is a fast robot that uses the Quick Boomerang as his weapon. His weakness is Flash Man's Time Stopper. The way the Time Stopper works on him is different compared with any other enemy in "Mega Man 2." Normally, the Time Stopper stops time until its energy is depleted, but does not allow Mega Man to damage enemies. Quick Man loses half his health automatically when the Time Stopper is activated.
Wood Man uses the Leaf Shield as his special weapon. It protects him from all damage while it is active. His weakness is the Atomic Fire from Heat Man. Metal Man's Metal Blades also works effectively on him. Both weapons are capable of killing Wood Man in the short amount of time he drops his Leaf Shield, which allows Mega Man to damage him.
Air Man fires tornadoes and use the fan in his chest to push or pull Mega Man. His weakness is the Leaf Shield used by Wood Man. The Leaf Shield, when it hits Air Man, does massive damage per hit. In addition, the leaves clog up Air Man's propellers, rendering his weapons temporarily inoperable.
Crash Man uses the Crash Bombs, a time bomb that attaches to its target with a drill, as his special weapon. He is weak to the Air Man's Air Shooter. He can take only three shots from this weapon. There are no special effects for using the Air Shooter beyond extra damage.
Bubble Man's special weapon is the Bubble Lead, a heavy bubble that rolls along the floor towards its target. He is also weak to Metal Man's Metal Blades. There is no special effect for using this weapon beyond doing extra damage.
Heat Man uses the Atomic Fire special weapon to fire flames at his target. He also turns into a fireball each time he is shot, torching anything he touches. His weakness is the Bubble Lead from Bubble Man. It does not do anything beyond additional damage, but it minimizes the number of time Heat Man turns into a fireball.