Radiant Silvergun

Level 3B is a relatively easy level to do this on. It's extremely short, and seeing as this can not be done in Training Mode, it only takes around 3-4 minutes to get there from the starting area 3A. So, you will be focusing all your attention on the Red enemies.

Now, if you play on Normal or anywhere below, you'll actually be 1 enemy short to fill up your chain, so you'll have to play this on Hard. Don't worry though, you'll barely feel any significant change on this level, apart from the suicide bullets shot from the ships during the very first enemy wave. The rest (if done correctly) will be destroyed before they're even considered a threat.

Some Tips:

- On Hard, you can actually skip two enemies, and still meet the required score. So, near the end of the level (just before the wall) you'll be faced against three red ships shooting blue rockets at you. It's possible to destroy them all by lining your Homing Plasma on the Middle & Left ships, but I found this incredibly tricky to consistently pull off. Therefore, skip one of the ships (The right one in my case), and simply use the Vulcan to destroy two of them.

- Close to the start (After the series of ships) there's a machine firing lasers from it's left and right, and red bullets from the middle. Make sure you destroy the lasers before dealing too much damage to the main body, otherwise it may blow up and destroy the two lasers, which will only count as 1 enemy.

- And obviously, practice this level in Training Mode until you're comfortable doing it for real. Like I said before, this level is really short, which means it requires little of your time to fully master. If you're unsure as to how to tackle certain parts, or how to efficiently use your weapons, download a replay to see how the masters do it. It shouldn't be too hard to follow as this level doesn't really have alot of ways chain.

EDIT: The video below should give you an idea of how to handle each section. Like I said before, you can easily find these replays in the game's leaderboard, but I figured I'd add an example anyway.
Also, this video is not mine, it belongs to tsnb30, all credit goes to him.

I wasn't able to do this on 3B Hard so I found an alternate method, not necessarily easier, but it was how I unlocked it. Here's the description for the video.

"This took me a couple of tries, it has to be done in Arcade- or Story Mode so you will have to play through a couple of levels to reach stage 2B. Practice in Training mode a couple of times until you feel comfortable. Can be done on very easy with low level Vulcan or the Sword."

Didn't mean to crash in the end of the video but I was so happy, I kept staring at my freshly earned achievement, haha.