This is one of the harder trophies to earn. Though players should increase the number of lifes they get to 5, and change the difficulty to easy. Then play through the game normally for the first level (hold UP to jump higher so you can reach levels, though doing this makes it so you can't shoot in mid air, so don't do it always).
Once you reach the second level, go to the upper right while on the platform until you find the corner with the open jail cells, Then you'll have to go through the level slowly falling down three times, til you reach the "Go" symbol, that'll be on the right side of the second level from the bottom. jump over the hole and walk over and you'll reach the boss area. Get the M power up if you need health and jump to the right. Now before you go too far to the right, save with a save state, so you can learn the fight and in case you lose all your lives.
Once you go farther right the fight will start, stay in the middle, shooting left or right depending on which ever way the jumping robot is. Ignore the other robot who doesn't jump as he won't hit you while you stay crouched, and you can change directions with out standing up.
Once the robots are killed once, they explode, but reappear and continue to attack, the jumping robot will start shooting three instead of one bullet, continue using the same strategy and eventually both robots will go down. This is a rather hard fight.
Once you beat them the stage will end. and you'll get the trophy.