On the first Dr. Wily stage, after the checkpoint there are two pipes which have weak respawning enemies. Use Jewel Satellite and stand on top of the pipes. It will take some time, but you will get extra lives and lots of bolts.
At the beginning of Hornet Man's stage, go right to the first ladder. Do not destroy any of the potted plant robots. Activate the shiled and stand on the second platform in between both robots. Remain standing there to destroy the missiles. Screws will automatically fall on Megaman.
Defeat the bosses in the following order to obtain the corresponding weapons that the next bosses are weak against:
1. Galaxy Man - Mega buster 2. Jewel Man - Black hole bomb 3. Plug Man - Jewel satellite 4. Tornado Man - Plug ball 5. Magma Man - Tornado blow 6. Hornet Man - Magma bazooka 7. Splash Woman - Hornet chaser 8. Concrete Man - Laser trident 9. Wall Shooters - Mega buster 10. Giant Machine - Laser trident 11. Blob Monster - Black hole bomb 12. Dr. Wily #1 - Mega buster 13. Dr. Wily #2 - Mega buster 14. Dr. Wily #3 - Plug ball
Splash Woman - Mega buster. Concrete Man - Lightning trident. Galaxy Man - Cement shot. Jewel Man - Black hole bomb. Plug Man - Jewel satellite. Tornado Man - Plasma ball. Magma Man - Tornado blow. Hornet Man - Magma bazooka.
Jitterbug (20 points) - Beat the game in 60 minutes or less. Invincible (30 points) - Beat the game without dying. Almost Invincible (20 points) - Beat the game without continuing. No Coffee Break (10 points) - Beat the game without using any Energy or Mystery Tanks. Peacekeeper (20 points) - Beat the game by defeating the fewest number of enemies possible. Conservationist (20 points) - Beat the game by using the least amount of Weapon Energy possible. Gamer's Day (20 points) - Beat the game 5 times in 1 day. Whomp Wily! (5 points) - Beat the game once. Destroyer (20 points) - Defeat your 1000th enemy. World Warrior (5 points) - Defeat every type of enemy. Trusty Sidearm (20 points) - Defeat the 8 Bosses with the Mega Buster. Blue Bomber (10 points) - Defeat a Boss without getting damaged.