Radiant Silvergun

First and foremost, you CAN change settings to make this achievement even easier. Choose Single Player > Arcade Mode > Normal Play. Now you will have a few options that you can alter. Change the difficulty to Very Easy, start with 10 ships, and extension every 1,000,000. You can even run out of lives and use continues.

I found it easiest to do on 3B. The game actually begins on 3A so it isn't the first boss you encounter, but the second. It is a blue ship with 7 different parts. To get this achievement, make sure you destroy all of the outer parts (3 on the left and 3 on the right) before going for the middle area. After he is destroyed, you will see the results screen for that level. If it shows 100 % on destruction, then you did it correctly and your achievement will pop.

This achievement is doable on the first boss easily, especially if you're trying to go for one of the Secret Achievements (Clear Level 1 using only a Sword).

The main trick is to keep to the sides and slash like crazy. You'll avoid most of the fire (you will need to move anyway, especially when it fires its main laser, as when it slows its spinning the rear of the ship will collide with you if you're not careful). The boss has 6 segments, two on each side as well as two in the centre, and your ability to hit the parts depends on what side it's on (whether it's upside down or right side up). When they're done, smash the bottom central part and you'll nab the achievement.

The only problem you have with this boss is that it is a timed battle. After a few minutes it will self destruct, which will rob you of the chance to get the achievement. If this happens you can go for the next boss (the one K4rn4ge mentioned) or try again.