Eventually in the Iceman stage you encounter a point where you try to get a 1-up but often miss it. When you drop down to the next screen (the one before the Big Eye), use your magnet beam and try to climb your way up and try to hop onto the offscreen platform where the 1-up is supposed to be. The instant you step on it, the screen will glitch and show you falling to the screen below and avoiding the Big Eye in the process.
While using a weapon that goes through an enemy, press the SELECT button (this pauses the game with out bringing up the weapon menu) when the weapon is making contact with the enemy. While the game is paused this way the enemy will continue to flash. When the flashing has stopped, press the SELECT button again to un-pause the game and the weapon will 'hit' the enemy again causing more damage.
You can repeat this trick with many of the bosses making them very easy to beat.