Gradius is pretty tough, mostly because your ship can only take one hit before it explodes. You can collect these orangey powerup things, though, and make your ship more maneuverable, get extra firepower, and get some shielding up.

But there's an easier way.

Just pause the game anywhere

Then put in the Konami Code:

Up, Up, Down, Down, Left, Right, Left, Right, B, A

Then unpause the game and you'll have some speed powerups, some Options (those orange things following you around), missiles, and a shield.

Just make sure you don't lose once you put the code in, since you can only do it once per game.