Don't stand still during this scene. The autogyros will drop grenades every time they fly over you and also occasionally drop a grenade for no apparent reason. Watch each autogyro carefully and, when one swoops down, jump stab it. You can destroy them just as easily as the first Boss scene.
To get all ship power-ups except for speed, at the game selection screen, select "Gradius". Then, at the title screen, press UP(2), DOWN(2), LEFT, RIGHT, LEFT, RIGHT, B, A. Then, Pause the game. This can only be done once.
Try to save your last three flamethrowers and only use each one when an enemy is almost about to hit you. If you're out of flamethrowers, simply stab at the regular soldiers and jump stab the karate soldiers.
Don't use weapons on the dogs. Before the first wave of dogs arrive, walk to the left of the screen but not to the edge where the dogs are just coming in, then rapidly press Stab. The white coat soldiers are just regular soldiers so don't worry about them. Before the second wave of dogs come in, run to the right side of the screen and duck stab the dogs and soldier. The dogs will start coming in quicker. Don't be at the center of the screen when attacking the fifth wave of dogs or else you will be in trouble. This is because soon as the barking stops for the fifth wave, the sixth wave will come in. You won't be quick enough to duck stab.
Earn extra points in the following events by performing the corresponding tasks:
EVENT - TASK Event #1 (100 Meter Dash) - Cross the finish line at the same exact time the other player (or CPU) does. A leprechaun awards you both 1,000 points. Event #2 (Long Jump) - Accomplish three identical jumps. A leprechaun awards you 1,000 points. Event #3 (Javelin Throw) - Get good speed and just before the foul line throw the javelin but do not release the throw button. The javelin goes up and off screen, hits an alien and awards you 1,000 points. Event #4 (110 Meter Hurdles) - Cross the finish line at the same exact time the other player (or computer) does. A leprechaun awards you 1,000 points. Event #5 (Hammer Throw) - Unknown. Event #6 (High Jump) - Hit the bar twice (foul) on the first 2 attempts, then jump the bar properly until you qualify. A mole will award you 1,000 points.
This is easily the hardest Boss scene. Use any remaining weapons immediately. When out of weapons, be sure to watch the flamethrower men extremely carefully. When they are at a distance, they will shoot the flamethrower at waist level. When they are near you, they shoot at your feet. While they are far away, wait until they shoot the flamethrower. If you don't, they will shoot at your feet and force you to jump closer to them (then they will fire at your feet as soon as you land, which will usually result in you getting burnt). Repeat this three times to complete the game. Note: This hint is for the first play through, not for the continued play after you have completed the game.