DEATH BY CUBE

Here a nice video I found for the achievement. They show 3 solutions and its the 2nd in the video. Really helped me a lot. Big thanks and credit goes to Rooster Teeth.

This is a fairly easy achievement to accomplish once you've figured out how to create an explosion in the first place.

In order to create an explosion, you must hold down the shield button (RT or RB) nd catch some shots in the shield. If you get the timing right, you can even catch your own. If you can avoid enemies long enough, you'll see a 3-second countdown timer. When the timer reaches zero, you'll explode, killing yourself in the process.

Make sure there's at least ten enemies around when you explode, and you've got the achievement. I found it pretty easy to do on the 4th level due to the abundance of both slow moving cubes and shot firing ones.

[Edit]
As Kronic1018 states, you can also catch enemies in an explosion caused by the explosives later in the game though I haven't personally confirmed that this method works for the achievement. I also haven't found it easy to use the explosives for getting kills much, at all. I still hold that the shield explosive is the easiest and earliest way to earn this achievement though I thank Kronic for the information.

If you're going for CUBE FINAL WORLD COMPLETE anyway, you don't need to spend any time specifically trying to get this achievement.
With the number of enemies coming at you in level 6-5 while you destroy bases, it's essentially impossible to complete it with a bronze score (let alone silver/gold) without popping this achievement.