Edit: I have found a better song to get this achievement with -- better, because it comes with Beat Hazard itself.

The track is "Beast Mode" by xKore, and is located in your beat hazard folder.

While Badp's answer works for the folks with BOSS RUSH, those folks who want to stick to just the base game of Beat Hazard are in luck: the same pair of boss ships can spawn in normal mode, and on normal difficulty, in a base game without any DLC whatsoever.

It may take a bit of parsing through your library until you find a song with both a "pair boss" spawn and enough time / lack of danger to kite them safely for 1 minute, but it's not outside the realm of possibility. To the best of my knowledge, it is okay to die after stripping both bosses, doing so won't invalidate the achievement (though you do want to make sure that it's not your last life).

In my case, I happened to have Dragonforce's Valley of the Damned handy, which features enough guitar power shredding to keep your guns nice and perky for most of the song. Disciples of Babylon was the song that ultimately got me the achievement, though, like most Dragonforce songs, it is a little on the long side.

The point to take away from this is that it's totally possible to earn this achievement in normal gameplay - experiment with your library, you might find an even better song!