If you want to continue after you go game over, type in NORIKO at the level select screen.
At the level select screen, type KAZUMI and you'll be able to continue after a game over. You'll lose your items though.
To get the good ending, you can only pause the game a certain number of times. The number of times are 1, 5, 9... (keep adding 4 to the count). If you get a game over, the counter resets.
In stage 6, reach distance 297 KM and enter the floor crack on the left. Get the Bracelet and leave the room. Once outside and with the Bracelet, reduce your speed and stay on the left of the screen. You need to jump and catch 5 fish (at least they fly directly to you). Just make sure to jump over the cracks on the floor, and as you jump, catch the fish. After 5 fishes, the Secret Bag will appear. If you miss one, don't worry, just catch the next one.
On stage 9, reach distance 305 KM and start jumping (more effective on 303-301 KMs). If done right, yellow wings (takes you to the bonus stage) will appear. Touch them and as soon as you start ascending, press the Space key 10 times. You'll then go to your bonus game as always, but once it ends and you go back to the stage, the secret bag will appear.
As soon as you start stage 13, stay on the left of the screen until the secret bag appears (around distance 580 KM or more).
On stage 14, jump in any of the cracks on the floor and while Penta is flailing his arms, press Left, then Right. If done right, the secret bag will appear.
While playing on stage 16, pause the game with F1 and press Up, Right, Down, Left. Go back to the game and a hidden bag will appear with the Armor.
On the specified distances shown below, fall into the crack on the floor and press Down to enter the hidden warp zones. Do note that you will miss items by warping.